I see more then just a couple possibilities:
1) Voynov retires. Contract gone, Kings would have similar rights as Kovalchuk.
2) Mutual termination of contract. Kings would not retain any rights.
3) Unilateral termination of contract by Kings. I don't think the Kings would retain any rights, but I'm not aware of a past case where a player was considered a defected player and the team could still retain rights after terminating the contract for material breach. If the Kings could retain rights in this scenario then they would expire after the 2016-2017 season, subject to the limited time opportunity to re-sign him I cover in (5).
4) Contract not terminated, Voynov is considered a Defected Player. KHL has an agreement not to sign NHL players in this situation, but maybe they make an exception due to Voynov's visa situation. If this happened then LA could choose to toll the contract or let it run as scheduled. No cap or contract limit implications for LA unless/until Voynov returns to the NHL during the remaining four seasons on his contract. If Voynov wanted to return to the NHL after the 4 remaining years on his contract expired then the Kings would have a limited time window to sign him--for practical purposes Voynov might as well be considered an impending UFA in that case.
5) Contract not terminated, LA agrees to allow Voynov to play in the KHL on "loan". To do this the Kings would have to put Voynov through waivers first before he could sign in the KHL. No cap implications, but Voynov would count towards the 50 contract limit. At this point there's a low probability any team would claim Voynov on waivers, so it might be low risk for LA to do this. The team would have to re-waive and loan him again each following season.