Should I stop talking to him. I broke up with him?

I was talking to this guy for a few months, but I felt like it wasn't going to work out, so I broke up with him. When I did, he became very verbally abusive, calling me derogatory names and cursing at me. Despite this, he still keeps messaging me, which confuses me.

Typically, he sends me memes or funny reels. However, when I send something back, he acts very unbothered. If he doesn't want to talk to me, why does he keep sending me things via text or DM?
Should I stop talking to him. I broke up with him?
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