The legendary beasts will all respawn (with full health) at the Burnt Tower after beating the Elite 4. Some people will purposely faint them and attempt to catch them at the Burnt Tower because, as they are not roaming anymore, it's much easier to catch them.

For more advanced trainers (people who play Pokemon competitively), they may save and then catch the beasts while roaming. (The beasts' stats are set when you first encounter them.) If their stats are under-average or if they have a bad nature, they soft reset (so the game loads the save file before catching them), and then faint the beasts. Upon finding them back at the Burnt Tower, they have different stats from when they were roaming.

The legendary beasts will all respawn (with full health) at the Burnt Tower after beating the Elite 4. Some people will purposely faint them and attempt to catch them at the Burnt Tower because, as they are not roaming anymore, it's much easier to catch them.

For more advanced trainers (people who play Pokemon competitively), they may save and then catch the beasts while roaming. (The beasts' stats are set when you first encounter them.) If their stats are under-average or if they have a bad nature, they soft reset (so the game loads the save file before catching them), and then faint the beasts. Upon finding them again (after respawning), they have different stats from when they were roaming.