Learn Portuguese (Portugal): Eles ficaram de subornar o juiz.

While ficar usually means "to stay" or "to become", the specific phrase ficar de + [infinitive] is a very common Portuguese idiom. It means "to agree to do something", "to arrange to do something", or "to be supposed to do something". It simply shows that a commitment or plan was made.

Could I just say Eles concordaram em subornar o juiz?

Yes, concordaram em literally means "agreed to" and is perfectly correct. However, ficar de is incredibly common in everyday spoken Portuguese for expressing plans or arrangements that people have settled on.

Does this sentence imply that they actually went through with the bribe?

Not necessarily. Because ficar de focuses on the arrangement or the fact that they "were supposed to" do it, we do not actually know if the bribe happened. It is frequently used to describe plans that were made but later fell through.

Since they are discussing a plan that might not happen, do I ever need to use the subjunctive after ficar de?

No. The preposition de in this expression must always be followed by the personal or impersonal infinitive form of the verb, which in this case is subornar. You never use the subjunctive immediately after ficar de.