You shouldn't really be afraid to save seed from hybrids. I've had a few of these in my garden but haven't done the selection that would be necessary to move things in the desirable direction.
I mean, the genes are all "in there" and they haven't come from some strange, alien place. It might be that some of those genetic characteristics are not something that you want in a tomato, let's say. Maybe one of the parents is kind of a disreputable critter but it has some great disease resistance. I suspect that often, the parent plants are fairly ordinary things - it's just their offspring that are different in some desirable way.
A lot of us have had tomatoes self-sow and volunteer. That usually doesn't work so well here; a volunteer usually doesn't have time to ripen fruit. Besides, a fair number of my tomato varieties are hybrids.
I give plants to my father and a volunteer showed up a few years ago. He left it to grow. Dad took a real interest in this healthy little tomato plant. Just before frost, it managed to ripen a couple tomatoes.
They looked just like the Sweet Chelseas I like to grow. When I pointed that out to Dad, he was kind of disappointed. Dad always was looking for something really special to turn up - optimistic that way.
I was pleased and should have grabbed a tomato then and there to see if I could "de-hybridize" Sweet Chelsea. What I might have done is to try to retain all of the things I like about the hybrid, while not saving seed from any plant that didn't measure up.
I see tomato growers do this sort of thing on a regular basis. Some use "5" as a magic number - if the seed is from a plant that is 5 generations from the hybrid, they have a reasonable expectation that it will mostly grow true-to-type. Bingo! A non-hybrid Sweet Chelsea! Maybe I could call her a "Sweet Charlie"

!!
Obviously, this wouldn't be an heirloom. It would be open-pollinated, of course. And, after some other "magic" number of generations - let's say 50 - somebody's grandkids could call it an heirloom

.
Steve
De-hybridized Big Beef Tomato seed, you can buy . . .