Thanks for the awesome compliments!
The way we thought of running out of space is a little bit more abstract:
1. The old man is running out of space for memories, he is sick with dementia and struggles with it.
2. The old man is hoarding due to his dementia, cluttering up the space in the apartment.
3. The rat is running out of space to move, as obstacles are closing in. (Poison, rat traps, old man, smoke are all becoming more frequent).
You can read a bit more about how we got to the idea here.