DRS Question

Just a quick DRS question that I assume has been answered before but have been unable to find an answer.

I was just wondering if I bought 10 GME shares at say $24 on Chase Investments. Then I DRS to computershare those shares when the price has changed to say $30. My understanding is that I've paid Chase and they have given me an IOU for those shares because they technically do not own those shares, so when DRSing they would then have to purchase shares at the current price to transfer to computershare. This would cause them to take a hit financially from my assumption. Am I missing something with this assumption?