The season of the show in which this happened was set in 1926. Basically, the Peaky Blinders (a British criminal organization) killed the father and brother of Luca Changretta, an NYC-based mobster. Luca comes to England with a dozen or so soldiers, infiltrates the Blinders' circles, and begins his retaliation.
Just when he thinks he's got Tommy (Peaky Blinders' leader) on the ropes, however, Tommy reveals that he reached out to other NYC crime families (and a guy in Chicago by the name of Alphonse Capone); because they're interested in Luca's lucrative cut of the liquor business, they've bought out his soldiers. The scene ends with the Blinders killing Luca as his former soldiers stand by and watch.
Could such an arrangement have realistically happened in this period? If so, how could any particular Mafioso be certain that he'd surrounded himself with loyal men?
An important distinction in your question: Changretta brings with him a combined force of Changretta Family soldiers (Made Men, as it were) and hired guns. Shelby makes a point of saying that- by the time of this confrontation- Luca’s family-bound soldiers have been eliminated, and he is currently only being supported by hired guns, who Shelby then reveals have since been either lured or coerced into betraying Luca Changretta.
So just to clarify, the situation is not “Could Made Men/family-bound enforcers be bought willy nilly” but rather “could hired muscle be persuaded to switch sides in the 1920’s underworld?”