Discarding a card in Phase 10 that allows the next player to go out
Yes, it is permissible ... and there are some occasions where you may find it to be advantageous. For example:


One person may be on the same Phase as you and well ahead of the others, but she may not have made her current Phase yet. If you feel she is close and you are not, it may be worthwhile to "end" the hand so that neither of you can advance.
Similarly, one person may be leading in terms of points, but he may have not laid down any sets or runs yet. It may be to your advantage to discard a card the next person can use to go out so as to (hopefully) stick the leader with a lot of points.


However, as is the case in many games, what is legal according to the rules may not necessarily be acceptable according to your group. Discarding such a card in this case may lead to cries of bias for the person to your left or against the perceived victim of your play. It may be wise to determine which is the primary concern in your group, winning or enjoying the game, before you decide how to play the hand.

Of course, this assumes that you have multiple cards to discard, and that you have not yet made your Phase. If you have made your Phase, then any card in your hand that the next person could play is also playable by you; you should play that one yourself and discard a different card. 

It may be the case that no matter what you discard, the next person will pick it up and go out, particularly in the Phases that require you to lay down 8 or 9 cards. For example, you may be on Phase 6, but you only have 8 cards to your run of 9, and the other two cards are playable. You draw a playable card: all three cards are playable, so you have no choice but to discard one. In that case, it may help to explain during scoring that you had no choice.