Have a Pokemon with the move called Mean Look, which Golbat is a primary choice to have this move. The move Mean Look prevents the Pokemon from fleeing or switching out during a battle and can be very useful in a battle like this. You cannot stop Mesprit from permanently fleeing, however. It is recommended to bring a Pokemon with any sleep status moves like: Hypnosis, Sleep Powder, Yawn, etc. to further the effect.
You could just use pokesav?
No, Scary Face is not a trapping move - it only decreases a Pokemon's speed, so it won't prevent Suicune from fleeing.
Mean Look is effective against the Pokemon Mesprit to prevent it from running away. Keep in mind that Mean Look ends when the Pokemon that used it is switched out or faints.
It will keep fleeing unless you have a Pokemon with Mean Look or something like that so it won't escape. Try catching a wild Golbat. The same is for Mespirit.
Have a Pokemon with the move called Mean Look, which Golbat is a primary choice to have this move. The move Mean Look prevents the Pokemon from fleeing or switching out during a battle and can be very useful in a battle like this. You cannot stop Mesprit from permanently fleeing, however. It is recommended to bring a Pokemon with any sleep status moves like: Hypnosis, Sleep Powder, Yawn, etc. to further the effect.
Mean Look prevents a pokemon from fleeing in from battle. It's useful when catching Cresselia and Mesprit, if that's what you're after.
You could just use pokesav?
You can use the Master Ball on any Pokemon you want to use it on, but I would use the Master Ball on roaming Pokemon, since they are difficult to keep them in the battle without fleeing. The roaming Pokemon includes: Articuno, Zapdos, Moltres, Raikou, Entei, Latias, Latios, Mesprit, and Cresselia.
they keep running around the region like mesprit
No, Scary Face is not a trapping move - it only decreases a Pokemon's speed, so it won't prevent Suicune from fleeing.
the Berlin wall
putting them in concetration camps
Mean Look is effective against the Pokemon Mesprit to prevent it from running away. Keep in mind that Mean Look ends when the Pokemon that used it is switched out or faints.
When Mesprit runs away in Pokemon Diamond or Pearl, it does not settle in one particular place. By using a certain Poke App (obtainable from the Poketch Company building 1F), you can track Mesprit's movements to eventualy encounter it again. Keep in mind that Mesprit will try to run away from you and will change places everytime you enter a new Route or City. Do not fly to where Mesprit is, as it will flee to the other side of Sinnoh. Learn Mesprit's patterns of movement and soon you will be able to encounter it. (Also note that Mesprit runs away during its turn to attack).
Mesprit roams Sinnoh.
It will keep fleeing unless you have a Pokemon with Mean Look or something like that so it won't escape. Try catching a wild Golbat. The same is for Mespirit.