It's clear from many episodes that the leapee does not have to survive to 1999. The most evident example of this is the time that Sam leapt into Lee Harvey Oswald. Since Oswald was killed by Jack Ruby (notably, both in the history Sam and Al remembered from the leap, AND in the one that came about as a result of the changes... where he saved Jackie), then there was no way he could survive to the proper time.
Should they have to? That's a bit beyond what can be answered here, as it's a fictional construct with whatever rules they decide on. Evidently, the creators decided that this doesn't need to be the case. They've also made other exceptions, such as Sam leaping into an ancestor in the Civil War in "The Leap Between the States", and Sam leaping into Al in "The Leap Back" (although both had brief explanations). This apparent inconsistency doesn't seem to be explained, but one could easily infer that the rule is actually that for time travel to occur (save for exceptions) the lifelines must intersect at one point of the leap, or that the displaced person simply goes to the only available "place" and that time travel doesn't have the restriction because violating "two objects occupying the same spot" is more of a problem than violating "within the traveller's lifetime". It's also possible that within the traveller's own lifetime is only a restriction for backward time travel, not travel to the future (which, considering we all do that every day, naturally would be quite a bit easier).
"The Leap Between the States", as well as plans for what would have followed the final episode suggest "within the traeller's own lifetime" may not have been a hard and fast rule after all...
From 10 things you might not know about Quantum Leap:
Bellisario later revealed that his original plan for the end to the show was to have Al and Beth as an old married couple discussing how they would locate Sam who had leaped again. As for that cliffhanger which was never shown, it saw Sam leaping into a space station in the distant future!
This suggests that Sam's not really bound to his own lifetime at all, at least not in a fundamental way, and so "time travel within his own lifetime" was a flawed theory... or that that may be a genuine limitation of the specific process (save the two noted exceptions), but not a rule for time travel itself.