There's two things about her kit that should really get some attention:

Her passive is pretty much worthless. The amount healed does little to nothing for her at any level, and it doesn't scale with her.

If I were to give a blind dagger toss at the idea board, I'd say change it to heal for some percentage of her missing health over the duration of Fury consumption, with the percentage based on how much Fury she had when she burrowed.

Example: "Upon burrowing, over the next 5 seconds Rek'Sai will restore a percentage of her missing health. The percentage restored is equal to a quarter of her Fury at the time of burrowing (100 Fury = 25% missing health)."

The other thing that should be looked into is the design of her burrowing, as the costs currently outweigh the benefits in most situations/cases.

I feel like she should gain a modified version of Twitch's stealth while burrowed. Reduce the detection radius from the Twitch's 700 down to only 400, but add a small particle effect at Rek'Sai's location when she's moving while not inside that 400 range. Additionally, have all wards (not just Control) show her icon on the minimap while she's within their field of view (only Control physically reveals her, still though). Lastly, if a champion hits her with a skillshot, have her become fully revealed and targetable until she leaves enemy vision (similarly to how Duskblade works).

Also, to snip the obvious abuse case of this in the bud, have enemy champions gain a hidden buff (no icon on their screen) while in range of Tremor Sense (even if it isn't actively revealing them to her) that stacks up over time (similarly to Baron's debuff). Once a certain number of stacks have been gained, put some kind of particle effect on the champion that lets the player know Rek'Sai is nearby and stalking them. Feels like... something... is watching us...

I feel like these burrowing changes would give her more of a fighting chance, without killing what makes her burrowing so unique and potentially awesome. I also feel like they wouldn't break her, because there's plenty of counterplay for her enemies to use against her if they're keeping mindful of their surroundings.

A note in closing, other parts of her kit might need slight number tweaks for this. That is an acceptable sacrifice for the greater good, though.