By alone I mean that they are not married, partnered or in a relationship.
I’ve heard that the number is increasing, and up to a third of this generation could die alone.
This isn’t exactly what you’re looking for but it might help you find your way to an answer - Eric Klinenberg wrote a book called Heat Wave: A Social Autopsy of Disaster in Chicago about the 1995 week-long heat wave that killed over 700 people. The title of an interview with him is called “Dying Alone”; he said in his book that a large number of those who died in the heat wave were elderly poor people who lived alone and were otherwise socially isolated. There might be some statistics there or in online resources to point you in a good direction.
Well, unless you and your spouse die in a car wreck or something like that, most likely ONE of you will have to die as a widow/widower…TRM (barring re-marriages, of course)
Even then, at the very end, one will have to die alone.
I think 1 in 3 is suspiciously low. Many people old people die relatively soon after their spouse has died, and those probably haven’t the time or the inclination to establish a new relationship. Even if everybody married at least once, and nobody divorced, 1 in 3 widow(er)s would have to remarry (before croaking) to get to the total down to 1/3.
ETA: read marriage/divorce as: begin/end a relationship.
Does the OP mean people who have never been married, in a LTR, etc.?