I can't answer this about the "Roman" Empire, but I can give you a few examples from Byzantine Times!

First, there's Theophobos. Theophobos was a Persian Khurramite (A sect that was rebeling against the Abbasids) who fled to the Byzantine Empire with some 14,000 of his men and was taken in by Theophilos, the Emperor at the time. Theophobos headed the Persian "Corps," made up of the Khurramites that had followed him and had converted to Christianity (This was good for the Byzantines, since, historically, nobody hates the Arabs quite like the Persians!). After the Battle of Anzen, where he saved Emperor Theophilos' life, his troops went to Sinope where, upon hearing a rumor that Theophilos had died, they proclaimed him emperor (interestingly enough, it supposedly happened in the way that Sassanians were proclaimed Shah). Theophobos was a friend of Theophilos and so the whole time he was "rebelling" he was actually talking to Theophilos secretly to try and get himself out of it. Theophobos was later pardoned, but then executed a few years later to prevent him from challenging Michael III's right to rule^1 :(

It's not "the troops," but during the great Nika Riots, the rioters proclaimed Hypatius, nephew of the late great Emperor Anastasius, as Emperor against his will (According to procopious he was dragged out of his room while he was hiding under his bed). He had no desire to be emperor and just wanted to be left alone, and when the Nika Riots were beaten down, Justinian was going to pardon him until Theodora supposedly talked him into it and he had him executed (The validity of this statement should be questioned, as Procopious was not a fan of Theodora and slanders her multiple times throughout his work). Poor Hypatius :(

[1] Skylitzes, John, A Synopsis of Byzantine History