No modern Russian or Soviet leader needed to, wanted to, or actually could "bug out". They either died in office (Stalin, Brezhnev, Andropov, and Chernenko), deposed more or less peacefully, and practically exiled (Khrushchev, Gorbachev), lost control due to illness(Lenin), simply forced to retire (Yeltsin), or actually killed in a coup (Beria). Of course, previous incarnations of SU/Russia still had some kind of order of succession, so there were at least someone moderately competent to take over if the current leader died or incapacitated. Something Putin simply eliminated to secure his position, to prevent anyone successfully challenging him, like what happened with Yeltsin.
As for running away to exile, the big question as usually is, running away to where? Who's powerful enough, to bother to go through all the trouble for you, for no reason? Putin literally made too many and too powerful enemies to slink away to some friendly regimes, which will shield him. Starting with the question of "friendly regimes" because he doesn't exactly have any thanks to his international antics.