Big Business and Big Government, which have eyed each other suspiciously over many decades, moved a perceptible step closer in the past week with the Carter administration's decision to support financial assistance for one of the giants of world industry -- ailing Chrysler Corp.

Ever since the early days of America's so-called free enterprise economy, there have been examples of government aid to the business sector. But most such assistance has been delivered not to specific companies but broadly throughout various sectors at particular moments in history to create jobs, save jobs or spur economic development.

Even during the Great Depression, government aid to business through the Reconstruction Finance Corp. was devised in such a way as to assume federal ownership on a temporary basis and not to bail out owners of the companies involved.

As the economy boomed in the years of consumer goods production after World War II, there was little reason for government involvement in business. With successive recessions starting in the late 1960s, however, some glaring weaknesses in the private sector have been exposed.

Chrysler is just the most recent example.

Before Chrysler there were the Penn Central and Lockheed, both in the 1970s. In the wake of the ultimate Pennsy failure, the government has been committed to spend well over $3 billion to rebuild a deteriorated Northeast rail system. Lockheed survived after receiving nearly $250 million in guaranteed loans, since repaid with interest to the Treasury. Now employees at the Milwaukee Road are seeking federal aid to buy that ailing railroad.

The likelihood is that with these corporate entities as precedents, more large corporations will be trekking to Washington for taxpayer assistance in the coming decade. If this happens, it will signal a fundamental change in relationships between government and business.

The following are some questions and answers about Chrysler's situation, including the role of government.

Question: Why is Chrysler asking for federal aid?

Answer: In simplest terms, the nation's third largest automobile manufacturer and 10th largest industrial corporation is running out of money to meet its payroll and pay bills. While no firm date has been projected when available cash will be down to zero, banks have decided they can lend no more funds and money could run out in the early weeks of 1980.

Working capital available to Chrysler has plummeted in the past 12 months from $959 million to $356 million as the corporation has reported growing losses from its business. In the July-September quarter this year, Chrysler had a staggering net loss of $460.6 million, more than any other business enterprise has lost in a full year.

The company has projected combined 1979-1980 losses at about $1.5 billion.

Q.: How did this cash squeeze develop?

A.: According to the company's management, the main factors are the costs of meeting federal regulations, gasoline shortages that altered car-buying habits last spring and summer and the current economic recession. In particular, Chrysler Chairman Lee Iacocca says regulations covering emission controls and fuel economy have been discriminatory against his firm. Because his firm produces fewer cars than giant General Motors Corp., the cost per vehicle of meeting federal standards is much more burdensome, Iacocca argues.

There is another cause of Chrysler's current problems -- a record of bad management in previous years by executives who did not plan ahead or spend for adequate factory modernization. Iacocca concedes the errors of the past but says it is in the national interest to permit him time to resurrect Chrysler as a truly competitive business enterprise. He has installed a new management team that consists mostly of former executives of Ford Motor Co., where he was president until a year ago.

Q.: How unusual is Chrysler's predicament?

A.: The auto company's declining fortunes are not unique in an economy where many segments of the manufacturing sector are showing signs of malaise. Not counting tax benefits here and overseas, both GM and Ford operated at a loss in the recent quarter. Ford's North American business has been unprofitable for several quarters. Overall the three largest auto firms are projecting $80 billion in capital outlays over the next seven years to modernize plants and retool for producing smaller, more-gas-efficient cars.

Q.: What aid to Chrysler has the aministration suggested?

A.: Under a proposed Chrysler Corp. Loan Guarantee Act, the Treasury would have authority to guarantee up to $1.5 billion of bank loans to the automobile company. In addition, another $1.5 billion must be raised by the firm, creating $3 billion in overall new capital. Outside financing would consist of new loans or credits, new investment in Chrysler (the firm is planning to sell some preferred stock) and disposal of assets not essential to basic auto production.

Typical of the outside aid required is that announced by Michigan Gov. William Milliken -- up to $185 million in loans to Chrysler, purchase of Chrysler land and a novel plan to offer Chrysler cars as prized in the state's fund-raising lotteries. Missouri, Delaware, Illinois, Indiana and Ohio, all housing Chrysler factories, are expected to offer other aid.

Q.: Why did the administration decide to support the loan guarantees?

A.: According to Treasury Secretary G. William Miller, there were several key considerations, including the risk of substantial unemployment and economic distress if Chrysler were forced into bankruptcy; the alternative costs to the government of unemployment compensation, welfare payments, loss of local taxes and federal revenues from a failure of the firm; the importance of maintaining "a strong automotive industry" in a world wide setting where this country must produce its own autos; and a desire to maintain a competitive U.S. industry.

Q.: Can Chrysler seek additional aid if the combined $3 billion package is not adequate?

A.: No. In an interview with The Washington Post last week, Miller emphasized that the proposed guarantee package "would be a one-shot deal." Barring unforseen disaster, such as war, there would be no point in adopting a plan that could open the door to additional guarantees or direct aid in the future, he said. If Chrysler is not successful in its five-year resuscitation plan, the U.S. government would have an initial claim on assets to cover its guaranteed loans.

Q.: When does the loan guarantee plan take effect?

A.: At the moment, it is just a proposal. A House subcommittee plans additional hearings this week, including scheduled testimony by Miller on Wednesday. After that, work will begin on drafting final legislation. Although several House members are outspoken in opposition, passage is expected this year. In the Senate, the Banking Committee will start hearings in mid-November. Although committee Chairman William Proxmire (D-Wis.) opposes the Chrysler plan, he has predicted passage by Congress.

Q.: If Congress passes the guarantee legislation, are Chrysler's problems over?

A.: No, they have just begun. The company has projected a $13.6 billion spending program over five years to revive itself, and the Treasury will have some voice in the current strategy of maintaining Chrysler as a company engaged in all lines of the auto business. Chrysler may have to cut back on its ambitious program. "They still have to prove themselves, that they can produce competitive products that will sell," said Harvey Heinback, a vice president of Merrill Lynch, Pierce, Fenner & Smith.