Or are we talking about one of the people involved being married already.

I think this makes quite a BIG difference.

If it's two single people then I guess from past experience this would mean that the relationship is over, unless of course one of them chases hard to get the other back.

Sounds to me more like the dumper is married and so has the high ground. Best of both worlds. Dumpee either does a 'fatal attraction - boil the bunny' job or retreats quietly. IF, on the other hand, the dumper tries to kick start the relationship again then I'd be very wary (unless I was prepared to live life on the edge for ever) and my first action would be to call his wife to confirm the situation.

Strident little monkey, ain't I. But I truly would do that.