It's not the idea of a meter that's expanding. It's the physical space that starts out a meter long/deep/wide that's expanding.
The meter-long stick you put into that space to measure it is still one meter long at some time in the future because the force that pulls the space apart (dark energy) doesn't pull on the matter that makes up the meter stick strong enough to overcome the forces that hold the stick together. But even if it did, the idea of one meter hasn't changed its definition. It's just the tool you used to measure one meter has broken.
The meter-long stick you put into that space to measure it is still one meter long at some time in the future because the force that pulls the space apart (dark energy) doesn't pull on the matter that makes up the meter stick strong enough to overcome the forces that hold the stick together. But even if it did, the idea of one meter hasn't changed its definition. It's just the tool you used to measure one meter has broken.