Will professors get dismissed for not actively doing research?

What is the binding power of research requirements upon professors and associate professors?

Without some specific agreement to the contrary, tenure means you can't be fired for doing insufficiently good research. Some tenured positions involve post-tenure review, which can weaken the notion of tenure by expanding the cases in which you could be disciplined or even fired, but this is not the default.

On the other hand, there are tons of other ways to enforce requirements. If a professor is not doing good research, they may be asked to take on extra teaching or service (which is reasonable: if they aren't spending time productively on research, then they should spend it on something else). In more extreme cases, they might never get a raise again, in which case their salary is gradually eaten away by inflation if they aren't near retirement. If the chair specifically wants to punish someone, they can assign them the classes or committees nobody else wants, give them the least desirable office, etc. In short, there are lots of ways a tenured position can become unpleasant, which gives the administration more leverage than one might guess from the definition of tenure.

I don't know of examples, but it's plausible. Remember that the purpose of tenure is to guarantee academic freedom, not to guarantee employment. While there is certainly an expectation of continued employment, it's not inviolable.

A particular institution's employment contract (or their faculty manual, if it has been incorporated to the employment contract, as is commonly done) will outline exactly how and when a tenured employee can be terminated. However, tenured faculty typically sign one-year contracts just like non-tenured faculty. Thus, it's more likely that the tenured faculty will be told they are being non-renewed "for cause". Some institutions make a distinction between termination and non-renewal, while others don't.

My graduate institution has this in their faculty manual:

[Termination of a tenure track appointment for] adequate cause may be academic incompetence, neglect of duty, a serious violation of the faculty member’s responsibilities as outlined in Section II of this policy, or admission or conviction of a serious violation of the criminal code, but the university bears the burden of proving that the alleged reason is adequate cause for termination

The relevant part of Section II referenced above is:

The faculty member has an obligation to fulfill his/her teaching and research responsibilities.

Where a specific department will likely have their own specific policies and procedures as to what constitutes the research responsibility. This can be very specific- the "research responsibility" might be defined as a certain number of publications, or a certain number of grant dollars. If the faculty member cannot meet that expectation then they are demonstrably not meeting the research responsibility as defined at their institution. Then it would be within the scope of the employment agreement to terminate the faculty.

A friend at a serious mid-tier research institution has told me that their bottom-line expectation is $250,000 of grant funding per year. Another friend at a good teaching institution that is trying to do more research has said that their bottom-line expectation is to apply for two grants per year. In my current department the obligation is phrased as a percentage of time. The research and scholarly obligation of the tenured or tenure-track faculty in the contract is described to be 50% of your effort (teaching and administrative duties is supposed to be the other 50%). If no such specific definition exists then it would be still possible to argue that a faculty member is not meeting their research obligation, but it would open up the department and university to potential legal issues.

Ultimately, this really comes down to a matter of practicality. Is it worth the time and the effort to remove someone who is severely under performing? If you have a lot of classes to teach and everyone is satisfied with just doing more teaching and less research then it's unlikely to be a fire-able situation. On the other hand, if you're in a competitive and aggressive department where you might be seen as "wasting" a faculty slot that could be better used by someone else, it would absolutely be within the realm of possibility.