'tackle' is a little stronger than that. It means making determined efforts to deal with a problem or difficult task. There's a sense of really getting to grips on the problem to solve it, from the 'cope' with it.
a 'detainee' is not necessarily a criminal, and would not be regarded as a 'jailbird'. An immigrant who has just arrived may be detained in quarantine if it is suspected he has a contagious/infectious disease; or it is suspected he is an anarchist and a threat to national security. If he has fled his home country because he is a wanted criminal, then he would be detained, pending extradition.