Can a 30-day tourist visa be extended in Thailand?

As Brandon mentioned, if they got a stamp for 30 days then they have no visa. They were given a visa exempt entry. This can be extended once for 30 days more at a local immigration office. They add on the days so there is no downside to applying early.

Because they were allowed entry under the visa exempt system there is nothing to stop them crossing a border exiting and re-entering Thailand for another 30 days at “no cost”. Obviously that would depend on whether they’re near a border and doesn’t include costs of getting to such border.

There is a limit of two land border entries visa exempt per calendar year.

If they fly somewhere else and return then there is no technical limit on how many times they can do that, except at some point the immigration officer is going to start asking questions why you’re doing that and could even possibly deny you entry.