Who were the unluckiest group?

I think Lynyrd Skynyrd takes the cake. Right in their prime, three of their members, including the lead singer, were killed in a plane crash. Yeah, they've done music since then as a band, but they never again got anywhere close to their glory days, and have pretty much been pegged as a nostalgia act under Lynyrd Skynyrd's name.

"Lives with no meaning go straight past you, like trains that don’t stop at your station."

That’s easy, Winger.

Without a doubt, one of the unluckiest & saddest story's in rock belongs to the group Badfinger. Widely hailed as the only worthy successors to The Beatles (so much so that many people belived they were actually The Beatles incognito), the band inadvertantly suffered decades of legal , managerial financial, & personal turmoil directly (& indirectly) related to The Beatles breakup & demise of Apple Records. The vast majority of their recorded output wasn't even released on CD until the early 2000s.

After Apple Records folded in 1973, Badfinger struggled with a host of legal, managerial, and financial problems, leading to Ham's suicide in 1975. The surviving members struggled to rebuild their personal and professional lives against a backdrop of lawsuits, which tied up the songwriters' royalty payments for years. Their subsequent albums floundered, as Molland and Evans alternated between co-operation and conflict in their attempts to revive and capitalise on the Badfinger legacy. Evans died by suicide in 1983, and Gibbins died from a brain aneurysm in 2005, leaving Molland as the group's only surviving member.

The Allman Brothers sure had their share of bad luck. First Duane, one of the greatest guitarists of all time, dies in a motorcycle accident and then almost exactly 1 year later their original bassist Berry Oakley dies the same way (via motorcycle crash) 3 blocks from where Duane had his wreck.

Every country band or act.
Listen to a few of their songs and you will find out why.