‘But the unclean spirit, when he is gone out of the man, passes through waterless places, seeking rest, and does not find it.'
In Matthew 10:11 the disciples were given power to cast out ‘unclean spirits' (elsewhere in Matthew ‘demons'). Jesus now takes the example of a man out of whom an unclean spirit has been cast. The use of ‘unclean spirit' is almost certainly intended to contrast with the Spirit of God, the ‘Holy' Spirit.
Like the man in Matthew 12:22 this man has been ‘healed'. He has been made clean, at least as far as having an unclean spirit is concerned. But the spirit is not necessarily finished with. It goes off, wandering in waterless places. Demons were regularly seen as living in deserts (Isaiah 13:20-21; Isaiah 34:14). It is looking hopelessly for rest. Matthew probably intends us to contrast this with the rest that Jesus gives to those who are His (Matthew 11:28). But unclean spirits can find no rest, and it therefore does not find it. There is no peace to the wicked, they are like the troubled sea that finds no rest (Isaiah 57:20-21).
This journey of the unclean spirit is probably intended to be contrasted with the journey of God's exiled people for whom in the coming days there will be water in the wilderness and springs in the desert (Isaiah 35:6; Isaiah 41:18; Isaiah 43:20). Even the screech owl may find rest in the wilderness (Isaiah 34:14), but not the unclean spirit.