There's a thread I saw sometime last week that describes how winning barely feels satisfying, but losing just feels disproportionately awful.
However, it could be entirely psychological, some people just react differently to certain types of stressful situations. It's absolutely happened to me on more than one occasion, to be fair, NEVER in ranked because I'm just not going to let my personal views interfere with competitive players, it's not worth my time or theirs, but people have bad days or even bad lives.
Sometimes you have to look at it from a different point of view, it's not necessarily that your teammate is no longer going to put in any effort, it could be that their confidence has been shattered and they think that no amount of effort they put in will be able to put them back at everyone else's level. They feel like they're now a hindrance to the game and can't really do anything because of how unbalanced the game has become. This isn't entirely unreasonable because the truth is even a few seconds off a trip back to your lane could mean the difference between keeping the pace, or an enemy who can dive you with absolutely no consequence (because turrets are garbage, essentially bendy straws, made of plastic, shooting spitballs).
In these cases, it's not anyone's responsibility to treat this person with special care, or baby them in any way, everyone's a victim of life's unfairness. But it doesn't hurt to help. Sure, some additional support to their lane can go a long way if they haven't really fed their enemy or if they have, just enough support to keep them from being consistently dived and killed without consequence. That way you and the rest of your team can start to feed off of a player who makes bad judgment calls from getting cocky after having been fed and mistaking that for extraordinary skill. At the very least, don't come crashing down on someone just because they've lost faith, understand that shit happens, and that some people play this game not just because they want to have fun, but because they need to escape the pressures of their real lives and then they can't handle when, suddenly, the game they wanted to enjoy becomes just another miserable reminder of how nothing they do is ever going to be good enough.
The easiest way to deal with it is to pay more attention to their positioning and coordination. If you need to back off of some teamfights, don't force engages, try to accommodate for some extra farming to catch back up. Most importantly, explain to them that you agree that it's a waste of time for them to try to force game-changing plays if they're too far behind to have a presence in teamfights or too weak to contest objectives, but the game isn't won by a single snowballed lane matchup (a lot of times it actually is, but this is assuming that the person on your team in ranked IS actually near enough to your skill level that they are neither intentionally feeding, nor foolishly over-extending once they've "given up").
Conversely, if you'd rather not deal with it so understandingly, buckle down on the player behavior and teamwork aspects and let it be known that the game isn't over and you'd appreciate it if they behaved more respectfully and less unsportsmanlike. You can report a player for negativity, just be straightforward and tell them that their negativity is affecting everyone else. Let them know that they can play safe and smart until the issue comes up to a surrender vote, and if they get outvoted it's only fair that they go with that diplomatic ruling, they chose to play a team game, so they need to be just as understanding of their team as you are of them. Tell them, as well, that as long as they don't intentionally feed, things will only get better for them, and that you're watching the map carefully to make sure they aren't trying to force the ending in their favor under the guise of "being caught off".
If they actually do continue with their unsportsmanlike conduct, you can mute them, continue to try your best and coordinate a 4v10 victory (4v10 assuming the one player is basically just a feeding trough for the enemy team) and report them for any offenses committed against the team.
