Since I doubt the Crusaders can take Cairo or Damascus without serious outside help (likely the Byzantines, who if resurgent are a problem in and of themselves) it's hard to see this happening. But I'll overlook that for now.
Let's say the taking of Damascus in a more successful second crusade. More than likely, It will become its own principality like Antioch or Edessa (and unofficially Tripoil). Of course, this principality will be even more exposed than Edessa, and will likely fall very quickly, at which point I doubt the Crusaders can take it back, or will even want to.
As for Cairo, they would really need help from several pillars to take it: 1. A strong fleet, like that of Venice, Genoa or Byzantium, to help take the Nile Delta and supply; 2. A quasi-agreement with whoever is the dominant power in mesopotamia to not attack, because the Arabians sure as hell will; 3. Support from the local Copts, to keep densely populated Egypt under their control. 4. A general crusade with support from a large area like Germany or France
Under any of these scenarios for Egypt, the crusaders will be rather reliant on foreigners, and will probably have to give some key trade concessions and/or cities to their fleet help (Byzantium would love Alexandria, Genoa and Venice to destroy each other's trade quarters and grow their own). They will also have to deal with whoever the new crusaders from western Europe are, and what they will want. In the end, what you are likely to see is a small Kingdom of Egypt, ruled from either Cairo or Alexandria. If it remains Christian, this state will quickly eclipse Jerusalem due to Egypt's wealth and population.
In either case, these conquests are not going to end up as vassals to Jerusalem, but rather more as buffer states. The idea in taking Damascus or Egypt (in the 2nd and 4th crusades) was to create a buffer zone so Jerusalem itself would not fall.