I've never been fired before, but I think it could be a valuable experience if you're under 30 or are working in a field where management has an industry-wide reputation for being fickle and employment is at-will/seasonal and inexpensive (i.e. if you're a waiter in a restaurant), but the idea that you should seek that out intentionally is crazy. If you're not 24 and you're not working at a chain restaurant or a beachside grille I'd be really careful about being fired for cause, especially if this work is in your long-term field of interest.
We always ask people whether they have been unwillingly terminated from a position in the past. It isn't always a deal-breaker (because sometimes you're just a lousy busboy when you're 16 years old and no one holds it against you if you're 34 and have a history of solid reliability), and sometimes it's a yellow flag, and sometimes it's serious and that alone derails a candidate.
In some instances, where it's clear an employee is the wrong fit, we'll leave the door open for them to walk out willingly. We cannot give them a great reference, but it's easy enough to say, "they did X and Y well, but it wasn't a great fit and they decided to move on". Plus, there's some satisfaction/relief in leaving on your own terms.
There is never a good reason to try to be fired for cause. There are tactical and strategic reasons not to have your contract renewed, to be laid off due to downsizing or a merger, or to be fired without cause (if your company and state allow for that), but to be fired for cause sticks with you.
They may not be lining up to fire you. This might be a disciplinary hearing, or a discussion about a mutually agreed upon (and documented) performance improvement plan, or even just a stern talking-to, if your reasons for concern are valid. But if they are, and they offer you the opportunity to resign first, take it. You leave with some more dignity, you save yourself the hassle and cost of a grievance or a wrongful termination law suit (if you think it was wrongful), and you move on. Short term expenses and debt may make unemployment attractive, but being fired for cause will mess up your employment prospects long-term and won't be worth it.