Flight

Those who had the means or opportunity could flee back to Europe or other safe havens when it became clear that the Frankish situation in the Levant was terminal. A lot of these escapes would be by ship.

Many population centres within the Crusader States were coastal because their existence was predicated on constant support and resupply from the sea (theoretically). This was true for both Acre (1291) and Tripoli (1289) and so both saw certain amounts of inhabitants take flight by ship to escape the final sieges. Of course this depended largely on your individual contacts or financial solvency and many would not have such a straight forward opportunity for escape.

Those who could get passage on a ship would not need to travel great distances to find respite however, as Cyprus was under Frankish control via the House of Lusignan (from 1285 under Henry II). King Henry himself took this exact route of escape as Acre fell to assault in 1291. Those with the prerequisite opportunities therefore could successfully escape to safety along this route.

Death or slavery

While the above scenario was viable and certainly did happen, we cannot ignore the fact that many thousands of Franks will have been left to fend for themselves when the final strongholds fell and that often meant death.

The last great cities surviving to the Franks weren't surrendered to the Muslims, which would sometimes result in agreements to spare inhabitants, but instead fell to storm and assault which in Medieval times had far less peaceful repercussions for captured populations.

At Tripoli and Acre there were massacres. At Acre, Tyerman writes that:

'Those who stayed were either slaughtered or captured to spend the rest of their lives as slaves or prisoners, the usual sequel to such military disasters'.

The situation was almost certainly not helped by long-remembered atrocities previously carried out by parties such as the Knights Templar. Whether sold into slavery or just immediately killed, the prospects of the average Franks left in the final mainland strongholds were almost universally negative.

Service

This scenario may also be of interest to you, illustrated nicely by a vignette in Barber's history of the Templars. It details two former Templar knights discovered living on the Dead Sea in 1340, many years after they had survived the fall of Acre. They had apparently saved their lives by entering into the service of the Sultan Khalil and gone on to have wives and families in complete isolation from the Frankish West.

This was not the most common outcome for a Frank after the fall of the Crusader States but it clearly did happen, if the Muslim lord willed it and the Frankish party had skills or attributes which were desired.

The former Templars were ultimately repatriated with their families to the Papal court and lived on peacefully, proving that in their case at least the swearing of their service to a Muslim lord had saved their lives.

Assimilation

I'm afraid this is the topic on which I am least informed, as I studied the military and administrative aspects of Crusade more than the social and/or ethnic. Somebody perhaps more versed in the local interactions could tell us if Frankish communities away from the strongholds were maybe able to assimilate peacefully and quietly into the surrounding population?

Further

I hope this was helpful; I'm not sure if you are particularly interested in a certain siege, state or year, (e.g. Edessa, Antioch) but if you want more specific information please ask and I'll try to get back to you!

For sources mentioned please see:

Tyerman, C. God's War, (2006).

Barber, M. The New Knighthood, (1994).

I think you would also appreciate:

Asbridge, T. The Crusades (2010).