In general, Trope Launch Pad (TLP) items that are still getting regular attention from the person who initially proposed them ("original poster" or "OP") should not be significantly edited or launched by someone else without the OP's permission. This is because, while TLP items (like ordinary wiki articles) are technically free for any registered user to edit, doing so can create problems, and can be considered pretty rude.
The "Up for Grabs" tag indicates that the draft is in need of a new sponsor.
TLP drafts are automatically considered Up for Grabs after at least two months of inactivity by the OP (original poster), but can also be designated as such by the OP if they've lost interest. If the sponsor is suspended, but is able to appeal their suspension, it may be unwise to throw a draft Up for Grabs just because the sponsor lost their privileges.
However, TLP drafts will automatically be placed Up for Grabs if the sponsor's account is deleted or permanently banned from TLPnote before the draft is launched. In general, if the sponsor is still on the site but hasn't touched the draft for whatever reason, sending a PM asking about the draft can help decide if it should be handed to a new sponsor or not.
It is a common faux pas to start a new TLP entry with the Up for Grabs tag. Doing so indicates that the sponsor doesn't care to work on their draft. We all get burnt out from time to time and it's okay to retire as a sponsor or allow other tropers to edit the draft if you can't, but tropes won't last long if their sponsor abandons them right from the get-go. If you don't want to work on your new draft, chances are others won't either. If you have a really good trope idea but no time to sponsor a draft yourself, consider putting it up on the Trope Idea Salvage Yard for someone (perhaps your future self) to pick up later.
Be aware that "Up for Grabs" does not mean "free to launch"—launching a draft, even one without a sponsor, without explicitly taking sponsorship yourself and announcing intent is called "rogue launching". Rogue launching is super rude, and it will get you suspended immediately.
When you take sponsorship of a draft, you need to rekindle discussion and resolve any lingering issues the previous sponsor didn't take care of—especially if the draft has been abandoned for substantially longer than the standard two months. While sponsors do occasionally abandon perfectly launchable drafts, it is far more common for an abandoned draft to need considerable work before it's ready.
If you're looking for drafts that have already been deemed Up for Grabs and don't need as much elbow grease, take a look at the TLP Adoption Drive. For more information on the rules of the TLP, see TLP Guidelines.