I recently came across this sentence
Die Delfine haben ihn umzingelt, aber nicht vor, ihn zu fressen.
(The ihn here refers to a small fish.)
How does the meaning of that sentence differ from
Die Delfine haben ihn umzingelt, aber nicht, um ihn zu fressen.
?
Your sentence seems to be meant as a shortened version of
Die Delfine haben ihn umzingelt, aber sie haben nicht vor, ihn zu fressen.
The repeated verb haben has been omitted. This is a common practice in general, but here it is bad style, because the first haben is an auxiliary verb, while the second haben is a full verb, moreover: it is only a part of the verb vorhaben that is actually being used here. So it is rather the same character sequence for two different verbs, and this shouldn't be shortened (except for an intended comic effect).
The difference to
Die Delfine haben ihn umzingelt, aber nicht, um ihn zu fressen.
is that the former talks about two separate (though probably related) actions (umzingeln and vorhaben zu fressen), while the latter explicitly negates that one action is the purpose of the other (that's what the um brings about).
