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 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.