[bikeshaving]

My guess is this is a subset of the halting problem (does this program accept data with non-halting decompression), and is therefore beautifully undecidable. You are free to leave zip/tgz/whatever fork bombs as little mines for live-off-the-land advanced persistent threats in your filesystems.

[machinationu]

it's not. decompression always ends since it progresses through the stream always moving forward. but it might take a while