Rootstock is much more vigorous plant than one on top (one that rotted for you). That plant on top is grafted in order to grow easier, or at all. Plants are grafted either because they are very slow growers, or lack chlorophyll and often will die because of it, if left on their own.

Rootstock will continue growing. There are few different plants used for rootstock. Very often, Hylocereus undatus is used (better known as pitaya or dragon fruit), but there are others. Plant will grow well and could get quite large. As dbarron said, you can leave it as is, or remove when bigger.

Now it has some decent sized roots sprouting. Is it still ok to just let it stay there?

Yes it is ok to leave🙂.

Just so you know Hylocereus have the potential to become a beast of a cactus. If given the right conditions of course. They are the genus of cactus that produce dragon fruit, and are native to Central and South America. So not the arid type. They will root on the forrest floor and grow up the trees like vines.

This is Hylocereus polyrhizus that has been manipulated and manicured to look like this.

All pics from Google.

Same with Hylocereus trigonus, this is how I’m assuming they are farmed for their fruit.

But this is how Hylocereus naturally grow.

I am telling you this so you know whatcha dealin with🌵.

Wow I had no idea!

Like Kara said they come from Central America and I saw them growing up a few trees in Belize but not as big as these in Hawaii and Maui.

They grow like a weed in the tropics. Here is a few I saw in Maui last year and marveled at the size and aggressiveness of these cacti.

A roadside stop to view the ocean and rocks below.

The ones I started a few years by slicing a store bought dragon fruit and putting on the surface of a pot of garden soil was easy. After my visit to Maui last year, I came home and moved my plants to a bigger pot with fresh soil and trying to stake them up so that they start to really grow. Too ugly to show but they've really started growing since then.

On the big island in 2014, I saw it up in the trees.

Thailand and Vietnam are #1 exporters of Dragon Fruit and the cacti come from Central America. It is indeed a small world.