If you have a keyword with a low search volume, and which isn’t driving any traffic and or conversions, it might seem like a good idea to add it to its own ad group through the SKAG functionality, and then add it as an exact match negative to avoid it driving any traffic. But logical as that may sound, it isn't always recommendable to do so.
For Google Ads, whenever a keyword has a Low Search Volume status, it becomes automatically inactive for auction time, and therefore won't accrue any cost. As these keywords will remain inactive until they get a reasonable amount of traffic, it would make no practical difference to add them as negative.
But take a look at the following example:
Say you have an exact match keyword that's made up of "Lake Tahoe Ski Cabins". This keyword has a low search volume and little to no traffic, so you don't want to have it as a keyword in your account, however, due to the lack of search volume, Google Ads still considers it as an inactive keyword.
If you maintain the keyword, it won't be considered into your spend, as it is still inactive. But if you add it as a negative, you could potentially be losing out on traffic that Google Ads might consider for, for example, "Lake Tahoe".
If you do decide to SKAG the keyword, we'd recommend the negative be added in the original ad group of the keyword.
If you would like to assess if a keyword should be added as an exact negative to an Ad Group, I’d advise you to check out the Traffic Sculptor. This optimization analyzes the search terms and the keyword data and suggests adding some search terms as an exact match negative keywords at the ad group level, ensuring the right ads show for each search query in the account.