With a trial of refusal able to overthrow as good as any decision of a single clan or even the clans as a whole I'm wondering if it is possible for a member of the not named clan to ask for a trial of refusal in order to stop the hunting down and killing of the survivors/descendants of that clans members?
Clan Wolverine had their Trial of Refusal already; the Trial of Annihilation is essentially a Refusal against the annihilation vote of the Grand Council.
The vote for Annihilation must be unanimous, and the victim may not appeal. The Trial of Annihilation is considered the accused's Trial of Refusal. If they survive it by defeating the forces sent against them, they are vindicated. Otherwise, they die.
The Clans: Warriors of Kerensky, p47
If someone with provable Wolverine descent were to show up later on and claim the right of Refusal of the Grand Council's Annihilation vote, they would not be able to, per Clan law.
The Trial of Refusal has its limits, however. First, the challenge must come from someone cited in the decision or within the appropriate body. Furthermore, Clan law forbids challenging the outcome of a Trial of Refusal with another Trial of Refusal but members of the council in question and those cited in the matter may stage additional Refusals.
However, though the first Refusal must be accepted, a majority vote of the council may deny the petition for a second challenge.
So in the case of our hypothetical Wolverine descendant, they a) were not "cited in the decision" (since they did not exist yet), nor were they b) "within the appropriate body" (since Clan Wolverine as a functioning member of Clan society ceased to exist in 2823). On that grounds they would not be allowed to present a challenge. They also cannot challenge the result of the initial Trial because that would be "challenging the outcome of a Trial of Refusal with another Trial of Refusal".
Since they cannot challenge the original Trial of Annihilation, they cannot challenge the hunting down of Wolverine descendants which is the lingering fallout of that Annihilation.
ilKhan Nicholas Kerensky declared a Trial Of Annihilation against Clan Wolverine, rallying all the Clans against the threat they posed to his dictatorship and vision for the Clans.
Since Nicholas was just making up an entire shamanistic culture and society to feed his megalomania, he could do whatever he wanted, and Clan Wolverine though this went against the principles of the Star League - hence, he made up a new Trial type to destroy them.
Nicholas went so far as to frame them for the atomic bombing of another Clans genetic repository, and rewrite Clan history to make them the bad guys in every scenario. As time went on, the narrative presented by Nicholas was taken as fact by all the Clans.
He was so successful, that a large number Clan Ghost Bear warriors who were found to have Wolverine DNA voluntarily committed suicide when presented with this information. Clan Ghost Bear even threw in against the Word Of Blake, 300 years later, after House Kurita provided very questionable intelligence pointing out that the WOB might be housing Clan Wolverine remnants.
At the current timeline of Battletech, the Clans have torn themselves apart in the Wars Of Reaving. The Inner Sphere once again is at war, every faction rattling the saber against the next. In the periphery, we are tantalized by Red Herrings such as the possibility that the Umyaads may have been part of the Clan Wolverine refugees, and a planet named McEvedys Folly shows up and disappears on some star charts. A mysterious group known as the Green Ghosts destroys explorers in the periphery.
The tale of Clan Wolverine is one of the greatest mysteries in the Battletech universe, and the one thing NEVER truly revealed in canon source. Wide speculation abounds - and the true fate may never be known unless someone involved in the Battletech genre gives one final gift to us fans!
(Even 1990s era Writing Guidelines for FASA had "nobody talk about Clan Wolverine" as one of the few rules!)
However, I doubt any Clan would respond positively to a Trial Request from someone representing Clan Wolverine - such a request would probably have to be discussed at Grand Council meeting, with the current ilKhan and higher ups present. With the Wars Of Reaving changing the Clan political landscape and the still-present hatred for Clan Wolverine, two possibilities immediately come to mind:
the current ilKahn uses the reappearance of Clan Wolverine to unite the fragmented Clans, and completes or declares a new Trial of Annihilation;
the Clan contacted immediately seek and destroy the returning Clan Wolverine members out of sheer indoctrinated hate, requesting reinforcements to do the job if needed
Also, if such a request is placed thru a proxy, like one of the Great Houses, the new Comstar, or someone in the Fortress Republic - any entity in contact with Clan Wolverine would definitely use this to their advantage, to reignite a war with the perceived advantage the presence of Clan Wolverine may provide.
Summarily, the inbred belief that Clan Wolverine is the ultimate evil and form of betrayal supersedes any Clan law, since they were subject to a Trial Of Annihilation, and not worthy of any treatment as a Clan, forevermore.
Besides, they are too busy fighting off Aliens and protecting the Inner Sphere to worry about the goings-on within.
I believe that most likely the Wolverines fragmented after the annihilation. That would mean the Uyamidds could be Wolverines and some could have made contact with Com star and been hidden. I think the likely hood of the Minnesota Tribe being of Wolverine origins is very good. Most survivors probably just blended into the rest of humanity. There is most likely no group or organization called th Wolverines today, they were annihilated.