The first pokemon in your queue will change. I haven't seen any other warning nor heard of one from other people.
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there isn't one, as this "feature" is really an unintended glitch since those pokemon technically can't run away.
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It's more likely that it's an intended failsafe so your pokemon don't disappear if the game crashes. If it was an unintended glitch they'd most likely have removed it altogether instead of still allowing us to have 100.
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I’ve had them disappear with less than 30 stored up. I had finished some quests but held off so I could complete the meltan quest when I got to that stage and they were gone after the feebas day. Everything got purged except for the feebas. Thankfully they brought the quests back
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I installed an app that allows me to track how many I have saved up.