Um, what do you mean “illude does not exist”? Sure it does. It’s just a tad rare these days. From the OED:
illude /ɪˈl(j)uːd/, v. Now rare.
Also 6 illud.
Etymology: ad. L. illūdĕre to make sport of, jest or mock at, ridicule, occas. to trick, impose upon, f. il- (il-1) + lūdĕre to play. Cf. obs. Fr. illuder (Godef.).
† 1. trans. To mock, make sport of, deride. Obs.
2. To trick, impose upon, deceive with false hopes.
There a bit more than that, but those other senses are not used any longer; only #2 is. Here are some citations to go with it:
- 1670 G. H. Hist. Cardinals ɪɪɪ. ɪɪɪ. 293 ― Full of hypocrisie and dissimulation, to lull and illude one another.
- 1872 M. Collins Two Plunges for Pearl I. iii. 64 ― They had allowed their imaginations to illude them.
They also mention the forms illuded and illuding; for example:
- 1745 Warton Pleas. Melanch. 185 ― The woodman’s stroke, or distant tinkling team··alarms The illuded sense.
- 1887 Athenæum 3 Dec. 745/1 ― They [women] come across unfavourable specimens of the illuding sex.
I’m not saying that you’re apt to skate on entirely thick ice if you were to use these, but illude certainly DOES “exist”, and means pretty much what you would think it means.