THIS IS A PERSONAL STORY of friendship between two women, one of whom is a friend of mine. Her husband moved to a new job in New York State last winter and she has been living here with their two children, trying like thousands of other people to sell her house in a mortgage market with 15 to 16 percent interest rates.

Her home is in a nice suburban neighborhood, the kind that attracts upwardly mobile parents with its good schools and large, new houses. It's the kind of home that wouldn't have stayed on the market long even a year ago. Two weeks, maybe, her real estate agent said. But it's been on the market since Feb. 15, priced well below the market value, and it has not sold.

Her husband has been living in a rented room near his new job. It has none of the comforts of home. She has been living here, keeping the house ready for showing. People come to see it every so often and they like it, but they can't come up with the financing. She worries that the separation is working a hardship on her husband. He also worries, not about himself, but about her. Each is working hard, he at his job, she at doing things like planting new flower beds in a home she's going to leave. Work is a way of coping with discouragement and loneliness. But it's a lousy way of living.

She has been to New York twice looking for houses. The first time, she and her husband found nothing. Toward the end of the day on her second trip, the real estate agent urged them to see one last house. "And of course it was the one we fell in love with," my friend says. It had an 8 1/2 percent assumable mortgage. It had a private suite for her father-in-law, who lives with them. Confident their house would sell soon, she and her husband put a contingency contract on the house in New York. The contract expries at the end of this month. The owners have offered to rent the house to them for the months of July and August, but unless their house here is sold, they will have to get a "bridge" loan for the down payment on the New York house and they would end up making two sets of house payments totaling about $2,400 a month. They don't have that kind of money.

Creative financing hasn't helped.They have decided to offer a rebate -- putting money in an escrow account so they can give the buyer $225 each month to help him make payments for the first tow years. "That," my friend says, "helps the buyer more than actually coming down on the price. I even thought of offering a higher commission [to the real estate agent], but I'm more interested in helping the consumer. We are all in this together." Last week she added a $500 bonus for the selling agent. Still, the phone hasn't been ringing.

Then, late last week a friend of hers came to visit. Theirs is the king of friendship you don't hear much about, the king, in fact, that a generation of adults variously indicated for being self-centered and self-indulgent supposedly has eschewed. It is the kind of friendship that takes time and generosity, two natural resources that we keep hearing are scarce.

It is a friendship that began through carpooling of children to ball games and when the other woman's husband died, says my friend. "I just felt I had to be there. This was like family. And I looked after her kids when she lost her father." She helped her friend put together and repair home appliances, always trying to walk the delicate line between helping out and taking over. She encouraged the other woman to go to work. She helped her handle the kind of depression where you want to crawl into bed and just stay there.

My friend knows what that kind of depression is like. She's been feeling about as down as she can get these days. And then last week the woman she had helped in her time of distress stopped by. "At first," my friend says, "I thought she'd come by to talk about a little neighborhood child who is having serious problems at home. But then she sat down and said, 'How much do you need to assume the loan in New York?'"

"And I said $60,000. And she said, 'Well, I can come up with $50,000.'"

"I knew," says my friend, "that the offer was completely genuine. She said let me know, because [her financial notes] will be maturing soon and I guess she has to know whether she wants to put them back in again. She wasn't talking about interest or anything. She said, 'All I care about is that I get the full amount back.'"

The woman brought another gift, a little prayer book with her maiden name in it, which she gave my friend, saying simply, "When all else fails."

"It was a novena to St. Theresa, the Little Flower," says my friend, "the saint who had such great love for the child Jesus that she would intercede with Almighty God for us.

"I was emotionally overcome that somebody cared that much, that she was willing to risk all her savings that she put aside to educate her children . . . I just couldn't believe it. People in your own family wouldn't do this. I knew she was my friend, but I never dreamt that anybody would care that much."