Last week, Melani Andrews walked into her local animal shelter and asked for "the oldest dog you have, and the one no one wants to adopt."

Staff at the Front Street Animal Shelter in Sacramento, California, knew just whom to introduce Andrews to. Jake is a 12-year-old dog who'd come in a couple of months earlier as a stray. He is suffering from bad skin, bad teeth and an untreatable, terminal cancer.

Jake and new mom Melani Andrews wore matching grins in their adoption photo. Front Street Animal Shelter

Jake's a "good boy," Front Street spokesperson Bobby Mann told TODAY. But because of his age and health problems, "he was overlooked."

Jake quickly got comfortable in his new home. Melani Andrews

Andrews immediately thought Jake looked "cute." The pair spent a little time together at the shelter before she rendered her decision: "He's going to come home with me," she said.

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It's been a hard year for Andrews. Her husband died in January, and her dog died a month later.

Andrews wanted to give a shelter dog a second chance, and also "wanted to share a life with somebody," she said.

That life is very sweet right now. Jake settled right into Andrews' home. He isn't well enough for trips to the beach but he's very fond of being in the backyard "and tormenting the dog next door through a hole in the fence," Andrews said.

The pair take short walks around the neighborhood, which suits them both. When done with that, Jake likes to curl up under a fleece blanket on a chair or on Andrews' bed.

He has a whole routine with the blanket, twirling it over himself just so, so he'll be tightly covered, like a little dog burrito. Andrews finds this extremely charming. She loves watching him sleep.

Jake's skin is more comfortable with coconut-infused baths. Melani Andrews

Mann, from Front Street, knows how hard it can be to find a home for a dog like Jake, who is so adorable and good, yet still has so many strikes against him. He hopes that seeing both Jake and Andrews so happy will inspire others to follow suit.

"We always encourage people to adopt senior dogs," he said.

When Andrews took Jake to her own veterinarian, he asked if she was aware that the dog is dying of cancer. She said yes, she's aware. Her goal is to make him happy, and comfortable, for as long as she can.

Jake's skin is raw, and Andrews gives him regular coconut-infused baths. She warms his water to room temperature because his teeth are so sensitive that cold water hurts. She moistens his kibble with some chicken broth so it'll be easier to eat. He wiggles when he gets his meals, and then cleans up the whole bowl.

Because his cancer can't be treated, Andrews knows there's no telling how long she and Jake will have together.

"But he's going to get a good life living here with me," she said. "I wanted to give a dog who didn't have a chance, a chance."