THE SUN SHONE hot on Friday as Winnifred Morgan, a once-respected college professor now destitute, stuffed her brain with escape reading to block out the pain and worry. A few paces from where she sat in a District park, a street woman with matted hair was washing up in a fountain, patting chilly water on her dirty face.

She was to Morgan a scary symbol, a specter of what could be. The street woman had slipped that one step down from poverty, and to Morgan, the vision was chilling.

More and more nowadays, Morgan, who has lost 45 pounds in the last year, is preoccupied with thoughts of food. "I've got one more serving of rice and some oatmeal left at home," she says. "But I dream of fruit juice and fruit. I guess it's the fruit juice I miss the most."

But food dreams are just one of the new habits this unlikely casualty of the economy has picked up in the last year.

"I realizing I can't use the washer and dryer," says Morgan, who was born in Oregon and brought up in Canada. "I need 75 cents to wash and 35 cents to dry, and I only have one towel. And I can't send [job] applications because I have no money for stamps. I've got clothes in the cleaners that I can't get out. And if I [have] . . . and interview, both my suits are tied up."

Winnifred Morgan was not always so hungry that an orange before bedtime or a glass of grapefruit juice upon rising was seen as a distant luxury. Until last year, this pleasant, clean and respectable-looking woman of 57 was a tenured assistant professor at Shippensburg State College in Pennsylvania. A specialist in Middle Eastern studies, her resume included studies at Oxford University in England and UCLA, and her doctorate was only a dissertation away.

Her bubble burst in May of 1980 when she was one of 125 professors throughout the state system who were fired in a buget-cutting move.

Initially, it seemed as if she would be able to survive. Until May, she received unemployment benefits, first from Pennsylvania and then from the District. She also won through arbitration a semester's pay from Pennsylvania.

But her luck changed when she made the decision to come to Washington in search of work after reading local help-wanted ads.

Since her arrival here in November, she's applied for over 100 jobs with no success. She says she'll take anything she can get. But she believes that her age and sex have teamed with the general state of the economy to work against her. Already, despair is creeping into her eyes and her drooping posture.

For four months, she slept on the floor in the apartment she rented because she could not afford to have her furniture shipped. Now she's afraid she may lose her furniture because she's unable to pay storage fees. In two weeks, she will have to vacate the center-city Washington efficiency apartment she now sublets. Meanwhile, St. Stepens and the Incarnation Episcopal Church at 16th and Newton has been giving her a daily meal and paid her last two weeks rent.

A few days ago, she reluctantly decided to apply for public assistance. She didn't get it. She was told she was ineligible because she is employable and has no minor children.

"Illogically, that was the most disappointing thing that has happened to me so far," she said. " . . . I'd worked 30 years and felt I deserved it [but] I still felt very bad about asking and about being turned down." Eventually, she was told, she'll be eligible for food stamps and Medicaid.

The whole experience has been eye-opening. The Bible Belt of Pennsylvania where she lived so comfortably so long was Jerry Falwell country, she said. "They all backed the Republicans, the Moral Majority. I think they think all poor are black. There's an awful lot of poor people who are not black.

"There are a lot of people falling through the cracks. In fact, I wouldn't say cracks, I would say chasms. I don't think the average American realizes -- and we're only starting this business of cuts . . . Young families are turning up for meals [at charitable organizations]. They're trying to avoid going on welfare.

"This is like the depression," she said. "This is what you did back in the 30's. I can remember our family going -- all of us -- to a soup line. And I can remember my father's agony over it because he was a dentist -- he lost absolutely everything."

President Reagan's proposed budget cuts worry her, but not only because of what she has undergone.

"Now if they throw all these people out of jobs, I think it's a delusion that they can find them [new ones] . . . If you're not an accountant or a systems analyst, what do you get?"

Her unspoken frustration was that, for the helpless like her, the coming cutbacks will leave even fewer alternatives.

"They want a strong nation. All right, I'm in agreement with that. But you don't get a strong nation by having lots of high priced military gadgets. You have to have people who are willing to sacrifice for the nation. If you alienate the whole bottom part of your population, how can you expect this country to be strong?"

Anybody without a big bank account or a family fortune, she says, is one step away from poverty. Ask Winnifred Morgan. She's stumbled down that step and can see the chasm gaping.