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Is there any reason why unconsumed_tail needs to be exposted?
I would suggest to instead introduce a boolean attribute data_ready than indicates that more decompressed data can be provided without additional compressed input.
Example:
# decomp = decompressor object
# infh = compressed input stream
# outfh = decompressed output stream
while not decomp.eof:
 if decomp.data_ready:
 buf = decomp.decompress(max_size=BUFSIZE)
 # or maybe:
 #buf = decomp.decompress(b'', max_size=BUFSIZE)
 else:
 buf = infh.read(BUFSIZE)
 if not buf:
 raise RuntimeError('Unexpected end of compressed stream')
 buf = decomp.decompress(buf, max_size=BUFSIZE)
 assert len(buf) > 0
 outfh.write(buf)
This is short, easily readable (in my opinion) and also avoids the problem where the decompressor blocks because it needs more data even though there still is an unconsumed tail.