His wikipedia page also has an amusing quote on the origin on this mission:

In August 1992, JPL scientist Robert Staehle called Tombaugh, requesting permission to visit his planet. "I told him he was welcome to it," Tombaugh later remembered, "though he's got to go one long, cold trip." The call eventually led to the launch of the New Horizons space probe to Pluto in 2006.

It's interesting that by sending his remains on that probe we basically guaranteed that at least some human remains will survive millions of years in interstellar space, unless of course, New Horizons collides with something(which I guess it will, given enough time?).

It would be fitting I think if aliens found his ashes considering he's was something of an ET evangelist and eventually claimed some of his mysterious sightings (green fireballs and glowing rectangles moving in unnatural ways) were probably of ET origin and its unscientific to dismiss this out of hand. Wiki:

Although our own solar system is believed to support no other life than on Earth, other stars in the galaxy may have hundreds of thousands of habitable worlds. Races on these worlds may have been able to utilize the tremendous amounts of power required to bridge the space between the stars..." Tombaugh stated that he had observed celestial phenomena which he could not explain, but had seen none personally since 1951 or 1952. "These things, which do appear to be directed, are unlike any other phenomena I ever observed. Their apparent lack of obedience to the ordinary laws of celestial motion gives credence."

https://en.wikipedia.org/wiki/Clyde_Tombaugh#Interest_in_UFO...

if we were to humanize alien that much, I'd see more likely for his ashes to become cosmetics for their gullible upper middle class.

There's a very moving passage towards the end of Stephen Baxter's Deep Future that talks about a space probe as potentially the last evidence of humanity's existence.

They will probably have a lot of really cool flybys before that happens.