After paying the fare, the cobrador is supposed to give you a boleto, your receipt. Cobradores usually have one of two habits. Some of them charge everyone as soon as possible. In this case you usually get your boleto without having to insist. Other cobradores are rather charging people when they are getting off. In this case you usually don’t get your boleto.
You can typically influence this behavior slightly. For example if you sit near the cobrador in the front of the combi, you can motion to him (or her) that you’d like to pay, without waiting until they bother to collect the money. The big exception to the rule is when you try to pay a china (50 cents). They might accept it, but that virtually always means that it goes into the “black money pocket” and it will not be an official trip and therefore you can practically forget about getting a boleto.
LimaEasy (which has a great page about traveling in Lima) explains that you should:
“…insist on getting the little ticket [as] this is not only your receipt, but also in case of an accident the insurance cover!”
Frankly I didn’t know that, but since reading this, I always insist on getting the boleto.
In order to know what to expect, I have found a great website called “Boletos de Micro de Lima”. On this website one guy has helpfully collected the majority of the boletos given in Lima’s combis. If I am not mistaken, some are actually more “historical”. But it gives an excellent idea of the diversity and the joy of collecting all these boletos. And it also gives me comfort that there are more people that have a certain fascination with combis in Lima.