People in Rome had something called patrons. If you had a patron, you were known as the client. Patrons were typically male and by becoming your patron expected you to give them political support by voting for them and encouraging others to as well.

In return the patron would provide clients with connections to influential individuals, food, and even legal support. One could ask their patron to help them in court. They would then send a lawyer to represent them. This is why poorer people in Rome were not defenseless. The issue was taken to a lower court, though the exact legal procedure varied between the Republic and the Empire.

It was quite common for wealthier Romans to take in poorer Romans as clients. The poorest of them could expect food at certain times of the day. As a way to pay back their respects one could also serve as a body guard to defend their patron from physical harm. This relationship also stacked, A patron could have a client, and that client could be a patron for another client. This was often seen as a social ladder and one would not want to be the client of someone lower than them. For example it was socially unacceptable for the King to be a client of someone. For more details research the Patron/Client system in Rome as it directly concerns legal representation.

I've read in SPQR by Mary Beard that you actually were not legally permitted to pay a lawyer directly. In practice, for example, a famous lawyer like Cicero, would accumulate favours from rich citizens he represented. So if you had no promise to later be able to do a favour, it might be difficult to find a decent lawyer to take the case. Cicero for example would buy various properties for low prices as compensation for representation. But as for what a poor person could do for representation, I don't know.