Is it possible to get "stuck" in Pokemon?
Well, yes you can get 'stuck', but it depends on the version.
For instance, in the first Gen II versions Gold/Silver/Crystal, you can get stuck.
Here's a gif from Pokemon Gold I made some moment ago. (the gif is quite big)
The main way I see it is when you are 'stuck' on an island where you require at least Surf to get off it and you don't have any Pokemon to use Surf or can teach it to since you released all the Pokemon who could.
In Red/Blue/Yellow, you have Cinnabar Island and in Gold/Silver/Crystal, you have Cianwood City.
As for Generation III games and remakes of previous games, there's a feature which prevents you from releasing some of the Pokemon, especially those which have Surf, Dive of Fly.
Here's another gif of Pokemon Emerald I made some moment ago. (that one's quite big as well)
The Pokemon will even keep the move in some cases (the Lanturn in the second gif refused to forget Surf at the move deleter). That means that as from Ruby/Sapphire/Emerald, there's a way you can go back and train your Pokemon until it levels up and be able to fight the trainer, though that might be extremely tedious (you'll perhaps have to save at every step when walking through tall grass/surfing) and go to a place where the wild Pokemon is of a reasonable level to train your current Pokemon.
You can get stuck in a battle with Lorelei in the Elite Four and not be able to Struggle your way out (all Generation 1 games)
To do this:
- Have just a pure Fighting-type Pokémon that knows Rage in your party (such as Primape)
- Deplete the PP of all moves aside from Rage
- Toss all items or deposit them into the PC
- Enter Lorelei's room in the Elite Four
You cannot leave Lorelei's room the way you came in, so you have to either defeat her in battle or black out. However, there is a problem with blacking out.
The only move that your Fighting-type Pokémon can use is Rage, which has a 100% accuracy and deals damage, then automatically is chosen on each subsequent turn. The only way to stop using Rage is to switch out Pokémon (which we can't do), have the Pokémon faint, or win the battle.
The AI in Generation 1 will always use moves that are super effective against your Pokémon's type. Lorelei's first Pokémon is a Dewgong that knows one Psychic-type move: Rest, which recovers HP. The HP recovered is greater than the amount of damage Rage can do. Thus Dewgong will never try to hurt your Pokémon and you will be stuck trying to attack it.
But what about Struggle? Well, it turns out your Pokémon will never do it. The first time you use Rage, 1 PP is deducted. But on subsequent turns, no PP is deducted when you automatically continue the attack. Thus you will never run out of PP and never use Struggle. Additionally, AI Pokémon in the first generation do not use PP, thus Lorelei's Dewgong will never run out of PP or resort to using Struggle.
There is technically a way out of this, but the odds are absolutely astronomical. There is a bug in Generation 1 where a 100% accuracy attack actually only hits 99.6% of the time. Therefore, there is 0.04% chance that your Rage attack will miss and you will have to spend another PP to attack with Rage again. However, this is only calculated on the first turn that Rage is used, not the subsequent turns. So if you ever successfully hit with Rage, no further PP will be deducted.
Because the base PP for Rage is 20 we need to miss the attack 20 times in a row in order to use Struggle (or if they have a PP up, more). According to the YouTube video "How to Escape Lorelei's Game Ending Softlock", the odds of missing Rage 20 times in a row are so infinitesimal that you have better odds of encountering 5 Shiny Pokémon in a row in Generations 2-5.
At any rate, if your Pokémon ever successfully lands a Rage attack against Lorelei's Dewgong, you will be stuck in an infinite loop and unable to end the battle.
I've legitimately gotten stuck on pokemon blue. I went squirtle at the start and had no pokemon to learn cut and spent all my money. There was no way to buy a pokeball to get a pokemon that could learn cut and I had no way to get to lavender town.
Then in the next major town you can't get back to that guy unless you have cut.