I am speaking from my knowledge of ancient history, so Hellenistic era and before.

There are several reasons why you might trust the enemy army besieging you to leave after being paid. A few that I can think of:

1. In the Mediterranean region, such pacts and oaths were sworn to with the gods as witnesses, breaking the oath would anger the gods and bring bad fortune upon you. Even tho this was purely a mental thing, it did seem to seal up some deals. Furthurmore, if a ruler/city was known for breaking their oaths, they would be less likely to be able to strike deals with anybody in the future, and worst case scenario would give other people an excuse to declare war on them, for not honoring the gods.
2. If an army was intent on sacking and destroying a city, they most likely would not take a deal in the first place. Often times, siege camps are running low on food and supplies, and quite often (as in the siege of Rome by Brennus) the besieging army would start spreading disease among the occupiers. In such a situtation, its really just a matter of who survives longer. Often times the attacking army would be happy to walk away with a profit, and not waste more men and money continuing the siege.
3. quite often to goal was to add the besieged city to the attackers existing lands of sphere of influence. A destroyed city is no use, and dead people pay no taxes. Getting the city to surrender before its destroyed is a win-win scenario, they get the money without having to loot the town, and the town itself has willingly agreed to surrender, saving you a bunch of money in continuing the siege.
4. (edit: just had another thought): more specifically to this era, there were a lot of short term gereral/leader positions in the ancient world (consuls, suffets[Shophet? spellings differ], archons, etc), and a lack of professional armies. In practice, this means you can have a general in command for a year, with an army raised in the spring and which expects to be home by the harvest. If the general's command is almost run out and he will be replaced, or the men are growing discontent and undisciplined, the general in charge would very often being open to terms of surrender to secure the victory during his time in power, and not give the glory to the person who is coming to replace him.

Now, with all that said, there is still no Guaruntee. And in times where they did not trust the enemy attacking their city, the citizens would resign themselves to fighting to the death (ie Saguntum), or where they took a sacred oath to defend their city to the last man, and stuck to it despite their own impeding doom (Abydos - not exactly the same scenario but it does show their devotion to their sacred oaths mentioned in point #1)