“About” is a preposition, so it must be followed by a noun. The simplest way to turn any verb into a noun is to add -ing, thus forming the gerund. In theory, it should be “boss’s” (the genitive), but in reality, native speakers tend to use the object case. Compare the sentence with a regular common noun: “They are worried about their boss’s temper.” 

In the sentence you posted, I would not use the genitive - it just sounds weird. If you want to use a conjugated verb, replace “about” with “that”: “They are worried that their boss may (/ might / will / could) replace them.”

Edited to clarify which sentence I was referring to.