It should be possible, I think–or plausible, at least.
Divorce. Man leaves wife for the younger model. Later, younger wife tires of the little blue pills and finds a younger man. But once the younger man starts to need the little blue pills, he resents his old wife’s wrinkles. Generations may shift, but this trend could go on forever in a long, unbroken line.
So imagine if each permutation, each couple forged in the ruins of the last, had children. One child, at least. What you would get, what you could end up with, is an endless string of half-siblings reaching from here into the dark backward and abysm of time. And what’s more, all of these children, from Timmy to Caesar, if it be, they could every one of them be seen as the same generation, half-sibs of half-sibs as far as the written word can read, and farther. Was that your great-great-grandfather, or your half-sister’s half-bro seven times removed?
Now imagine an object, like a watch or a quilt. An heirloom or a toy, doesn’t matter. Each half-sibling (or one of the bunch) makes a vow to the last to pass on the object to the next half-generation, when it arrives. So out of the tragedy of death or divorce, a living history breathes affection into the future, and the legacy continues until the last bro or sister survives both parents, further childless, and the quilt or toy or time-piece is buried in their grave.