Ndtyhij

I think I am remembering 2 different stories but it was a long time ago so I might be thinking of (and mixing up) one story in my memory somehow.

First is about a vampire who is the last living thing on earth. All other life is gone and all the immortal vampire has to look forward to is getting hungrier and hungrier as the years pass by.

The other memory is of a vampire ends up in the far future (don't remember how) is hungry and goes out hunting. Follows a young female of the now dominate species into a dark place, attacks her, bites her neck, and discovers that she, and all the other life on earth are plants! No animals, no blood!

That's about all I remember except it was maybe in the 70s or 80s and both(?) were short stories.

The latter one might be Fredric Brown's "Blood" (text available here), but the attack on a young female (actually a literal bitch), and the revelation that the current era's people are plants, are separate.

In their time machine, Vron and Dreena, last two survivors of the race of vampires, fled into the future to escape annihilation. They held hands and consoled one another in their terror and their hunger.

In the twenty-second century mankind had found them out, had discovered that the legend of vampires living secretly among humans was not a legend at all, but fact.

There had been a pogrom that had found and killed every vampire but these two, who had already been working on a time machine and who had finished in time to escape in it.

Into the future, far enough into the future that the very word vampire would be forgotten so they could again live unsuspected--'-and from their loins regenerate their race.

"I'm hungry, Vron. Awfully hungry."

"I too, Dreena dear. We'll stop again soon."

They had stopped four times already and had narrowly escaped dying each time. They had not been forgotten. The last stop, half a million years back, had shown them a world gone to the dogs-quite literally: human beings were extinct and dogs had become Civilized and man-like. Still they had been recognized for what they were. They'd managed to feed once, on the blood of a tender young bitch, but then they'd been hounded back to their time machine and into 'flight again.

"Thanks for stopping," Dreena said. She sighed.

"Don't thank me," said Vron grimly. "This is the end of the line. We're out of fuel and we'll find none here-by now I radioactives will have turned to lead. We live here. . . or else. "

They went out to scout. "Look," said Dreena excitedly, pointing to something walking toward them. "A new creature! The dogs are gone and something else has taken over. And surely we're forgotten." The approaching creature was telepathic. "I have heard your thoughts," said a voice inside their brains. "You wonder whether we know 'vampires,' whatever they are. We do not."

Dreena clutched Vron's arm in ecstasy. "Freedom!" she murmured hungrily. "And food!"

"You also wonder," said the voice, "about my origin and evolution. All life today is vegetable." He bowed low to them. "I, a member of the dominant race, was once what you called a turnip."

There's a Roger Zelazny story in which the last human alive is a vampire.

Fritz is a vampire, which is a terrible and tragic thing. He is so
undernourished that he cannot move about, but he cannot die either, so
he lies in his casket and dreams of times gone by. One day, he will
ask me to carry him outside into the sunlight, and I will watch him
shrivel and dim into peace and nothingness and dust. I hope he does
not ask me soon.

(the narrator is a robot, who happens to be a sort of robo-vampire himself)

The story is The Stainless Steel Leech.