I would remove the yellow stem and change the water. I might even go so far as to remove the whole thing from the pot to check and rinse the roots and rinse the stone and pot, then replant it. All depends on what that yellow stem and its roots look like when you get it out, if it is rotted and mushy it is likely some of the mush remains in the pot, something you don't want left there.

Remove yellow stem, it's dead nothing can be done to save it.

You should take it out of the container and inspect the roots. Healthy roots should be white, beige, or orangey,

if you see black or mushy roots they need to be removed, then cleaned, if they are slimy but otherwise healthy should just be cleaned.

To clean, remove plant from its container and rinse its roots under a faucet, use your hands to rinse the roots, wash any slime off, untangle any roots if necessary, dont worry about hurting the roots, its a fairly hardy plant, as long as healthy roots are not ripped off it's fine. Also make sure the pebbles are clean and not slimy.

You should replace all of the water and gently rinse the roots as well in the plant at least once a week. Its better to spend 5 min each week caring for it than scrambling to save it after it standing forgotten for a long time.

If you plan on keeping it long term consider eventually planting it in potting soil and keeping it moist, that would be least amount of maintenance and make it the happiest.

How is the plant now?