We see that when Jacob opens the Newt's suitcase in Fantastic Beast and Where to Find Them some beasts escaped, few beasts compared to the amount that he has inside the suitcase. Why didn't more escape?
Also, multiple times in the movie, Newt leaves the suitcase open, why didn't any beasts jump out then?
It's probably because none of them had any reason to. Each of the creatures were well looked after inside the suitcase by Newt, in environments that were ideally suited for them.
The only ones that did escape had specific reasons to do so:
Niffler: looking for gold to collect, was trying to escape even when the suitcase was closed.
Erumpent: the glowing rhino creature was in heat, and was seeking a mate, which is why it responded strongly to the pheromones that Newt used (and later Jacob got all over himself). It likely escaped in order to try to find another erumpent to mate with.
Murtlap: the little pink dog thing seemed to be pretty aggressive, may have just reacted when Jacob (an unusual human) opened the case, and it leapt at him. They do tend to bite (and eat the feet of) humans that come near them in the wild. It didn't go far once it was outside of the case, which means it was likely just being territorial.
Occamy: not too sure about this one. Only one bird/serpent thing escaped when all of its siblings stayed put. May have simply been more curious or adventurous than the rest. It did seem incredibly interested in the bug held out for it to eat, so may have just been looking for different things to try to eat rather than the things that were provided for it.
Demiguise: the invisible monkey creature was babysitting the Occamy. It was bringing it food and various other things from around the city. As it could see the future, it's possible that it saw the Occamy causing destruction in the city or dying if it was let out on its own.
All the info about the creatures is from this question on SciFi.SE.
Why would more escape? They'd need to recognize the exit for starters. And only highly mobile creatures would be running around. The niffler, that's one that's very incentivated to escape, he can only grab gold outside after all. But every other creature, well it's just a matter of luck if they bump against the exit.
