As long as it has toughness 1 or greater again after the spell or ability resolves, it will survive
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Generally I shy away from effects like this, especially with +1/+1 counters just not being very good if that's the focus of your deck
It not only works like a removal spell, helping you push through more damage or make blocking a Fathom Fleet Captain impossible, but given another turn, you can potentially keep your opponent from getting their creature back while growing your own army