Agents don't need to go out of their way to find clients. But it's quite common for frauds to buy mailing lists of writers and go fishing. Unless you have published something, or otherwise have a reputation as a writer, no real agent is going to contact you out of the blue. Agent's contract has a time limit. Agents used to work on a handshake basis, but nowadays even good agents often have contracts.
Agent claims sales to a vanity press.
A vanity press is one where the author pays to be published. Agent asks you to put up your money in advance. What I tell you three times is true. If an agent does any of these things, go somewhere else. It's just not worth it.