The colloquial phrase to come to a sticky end, and its variants, mean to die, or to come to grief, in violent or exceptionally unpleasant circumstances.

In this phrase, the adjective sticky means unpleasant.

The phrase to come to a sticky end occurs, for example, in Country diary, by Robin Page, published in The Daily Telegraph (London, England) of Saturday 28^th December 2013:

I have had foxes as pets in the past—they were wonderful “friends”—teaching me much, but remaining in effect “wild animals”. Even in captivity they could not be house-trained and they could only be let loose when the free-range hens were shut up.
Most came to a sticky end. One was shot, one was killed by a dog and, yes, I have spilt many tears for lost foxes.

The earliest occurrences that I have found of the phrase to come to a sticky end and variants are as follows, in chronological order:

1-: From The Warwick Argus (Warwick, Queensland, Australia) of Saturday 27^th November 1897— Thomas McIlwraith (1835-1900) was an influential businessman and a prominent figure of colonial politics in Queensland:

The other passage of special interest in Sir Horace’s speech was in reference to Sir Thomas McIlwraith’s position as a member of the Cabinet. Ministers have at last arrived at the conclusion that it is not desirable that he should continue a member of the Executive, even in name. Sir Thomas has received a friendly hint to this effect, and Ministers now await his resignation. If it is not forthcoming within a reasonable time the equivalent for a writ of supersedeas will issue. What a “sticky” end to such a “rockety” career.

2-: From Chapter 43 of At a Man’s Mercy, by Meta Simmins, published in The Daily Illustrated Mirror (London, England) of Tuesday 5^th April 1904—Miles Farmiloe was shot dead earlier in the novel:

“You were there—and surely you remember it?—with your friend, Miles Farmiloe.”
“Miles Farmiloe?” he repeated. This time there was no possible doubt that his face had darkened considerably. “Ah, yes, I remember Miles Farmiloe. Poor chap! That was the fellow who came the other day to such a sticky end.”

3-: From the review of The Country Girl, which was produced by “Mr. Williamson’s Royal Comic Opera Company at His Majesty’s Theatre”—review published in The Telegraph (Brisbane, Queensland, Australia) of Wednesday 3^rd August 1904:

Mr. George Lauri created no end of amusement as Barry, Geoffrey Challoner’s “man.” In the ballroom scene he was distinctly clever, and his warning that Madame Sophie, if she did not mind, would come to a “nasty, sticky end,” was the signal for screams of laughter.

4-: From the column The Bran Pie, by Adrian Ross, published in The Tatler: An Illustrated Journal of Society and the Stage (London, England) of Wednesday 28^th September 1904:

The autumn manœuvres have come to an end—if not to what has been called “a nasty, sticky end,” at least to a sufficiently disagreeable one, for the invaders of Essex began with sea-sickness and ended with the same. The landing was, indeed, unresisted by the army and actively assisted by the navy, and yet it was sufficiently tedious and uncomfortable. On the whole, the experiences of the manœuvres go to show that except by the previous capture of a fairly commodious harbour, landing an army in a hostile country is an extremely dangerous operation.

5-: From a letter to the Editor, by a person signing themself ‘B.’, published in The Indian Daily News (Calcutta, West Bengal, India) of Thursday 3^rd August 1905:

Has my friend ever heard tell of an eminent sportsman, named Humpty Dumpty? The history of his life and character is set forth with more or less detail in one of the lesser English classics. Now Humpty Dumpty was a person who thought that he knew everything (he came to a nasty sticky end eventually—but this quite by the way.)

6-: From Prairie Creek News, published in the Central City Record (Central City, Nebraska, USA) of Thursday 12^th April 1906:

In last week’s Record we noticed something about a Cuming County mail man whose horse drowned in the mire before its owner’s very eyes. As for us, we have no such marvelous incident on record, but […] the mail carrier takes every precaution to keep his nags from getting fast in the mire and is seemingly afraid he will come to the same sticky end as that poor unfortunate horse in Cuming County.

7-: From the account of a golf competition at the Victoria Club, published in The Argus (Melbourne, Victoria, Australia) of Monday 8^th June 1908:

Albert Yuille, the club champion, had every chance of equalling M. Scott’s record of the course, but came to grief at the seventeenth, and to a nasty, sticky end in the eighteenth waterhole, both of which adventures cost him seven strokes, and all chance of a fine card.