It also depends on who got dumped and who did the dumping. For instance, a co-worker of mine, "Sammy," got dumped by his fiancee, "Denise" (they'd been together almost ten years). Sammy's best friend since high school, "Vince", then pursued Denise, not unlike this Bill/Rick situation, offering "dinner to cheer her up" and "someone to talk to" because "she's still my friend too!" Within a matter of weeks, Vince and Denise have decided to move in together because "she doesn't have anyplace else to go" and Denise is telling everyone she knows (including me) that she and Vince are soulmates and this whole situation has been destined because they're meant to be together. The two of them disrespected Sammy horribly! For months after, Denise and Vince would show up at places where they new Sammy would be (often with a group of us co-workers who'd gone out for a beer). Sammy would usually make a polite excuse and leave when things got to be too much (D & V liked to engage in showy face sucking marathons), but was always very classy about it. Denise and Vince, on the other hand, really seemed to enjoy trying to taunt Sammy, and when anyone called them on their crappy behavior, they'd make a big too-do about "they aren't together any more!" and "Sammy's just jealous and bitter!"
You know the saying, with friends like that, who needs enemies? After watching all of that unfold, I refuse to make excuses for friends who hook up with friends' exes. It's crappy.
(Lucky for Sammy, Denise and Vince eventually moved away, and two years later, after some dates that went nowhere, Sammy met a sweet woman while training for a marathon. They're getting married in the spring.)