When an SSD runs out of blocks that can be erased and reprogrammed the last attempted write will fail and the drive will enter a read-only state. It will probably not be able to support a running OS, but can simply be stuck in another machine and have its data safely extracted. A typical consumer SSD should be perfectly readable for at least a year before the cells begin to lose charge and the data lose integrity, so if you can't find a PC within a year to put it in then you're out of luck :P All of this is in contrast to HDDs, which can become difficult to read from once they fail because they often fail mechanically.
Whether your SSD will go read-only at 0% remaining life is impossible to know until you get there, but it's entirely possible that it will last some time longer. The average program/erase cycle count per block is rated at 5000, but this is simply a rough specification and a lot of blocks will sustain many more cycles than that. Keep a track of your Program Failure Block Count and Erase Failure Block Count SMART attributes. Once these start to climb sharply you will want to think about getting a new drive.