Puppies are often the first dogs adopted from animal shelters, while senior or terminally ill canines are left waiting for days or even months for someone to notice them. This New York City-based group is working to ensure these exceptionally vulnerable dogs go to a forever home too — even if it's just for the short time they have left.

About six years ago, "Foster Dogs, Inc.," was contacted by local shelters that needed help with the elderly or ill dogs in their care, said Founder and Executive Director Sarah Brasky. She realized that there was a real need for a specialized "end of life" foster care program for dogs that might otherwise have trouble finding forever homes.

The nonprofit, which has been operating since 2009, works to connect rescue organizations, adopters, fosters and others to help animals in need. It is also dedicated to, "the advancement of education about fostering and rescue, and to creating a positive and inclusive foster community," according to its website.

April is one of the 55 dogs who has gone through the program so far. NYC Pet Photographer

Brasky decided to do something to help these dogs spend the rest of their days out of the shelter and the "fospice" program was born. The initiative, which she said was inspired by a similar one by the ASPCA, was dubbed "Fospice" — a combination of the words foster and hospice.

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"These are dogs that are elderly and/or terminally ill, who don't deserve to die in a shelter. They need so little, and give so much love in return," said Brasky. "It's all about just providing comfort and a loving home."

While some of the dogs are just given "gifts and goodies" to lift their spirits, the majority of the pups are brought to a Fospice home, where they will live out the rest of their lives with someone who loves them. Fospice homes and families often receive the monthly dog subscription box "BarkBox," treats from local pup bakeries, financial support for the organization and even a sweet professional photoshoot.

The New York City-based group also offers ongoing support for the owners, as it can be difficult to grapple with only having a dog for a short time. "That's really the tough part is when somebody will commit to spending many months with a dog that they may not have known anything about," said Brasky. "They just know the dog is towards the end and they just need a loving home."

The group has a "Foster Roster" database, with over 3,000 residents in the New York area who are interested in fostering a pup in need, Brasky told CBS News. When a potential foster indicates interest in the Fospice program, the group reaches out to them directly to see if they're a good match.

Fifty-five dogs, coming from 22 rescue groups, have benefitted from Fospice over the years and "innumerable" people have volunteered to take these special pups in, according to Brasky.

"Knowing that you have a shorter amount of time with a Fospice, it's so important to make every single day count," said Tracy Slagle, who was fostering her second dog through the program — a 19-year-old named Albie. Slagle completes bucket list items with the dogs she cares for in the program, including sharing a Thanksgiving meal, taking a pup to Nathan's Hot Dogs and even kayaking with the canines.

The "Fospice" program was named "Chloe's Fospice Friends" in 2018 after the late Chloe Kardoggian. Real Happy Dogs

Oyinda Adefisayo, a first-time Fospice parent, said she lets her pup Wiley eat "whatever he wants to eat," and joked he "gets away with everything." The 7-year-old dog was diagnosed with an aggressive cancer.

When the dog dies, the program covers all end of life expenses as well. "Even though it's really emotionally draining at times, especially when the dog has to pass away, after the person has time to mourn, almost all of them have come back," said Brasky.

Slagle echoed her sentiment, telling CBS News"I can't imagine not doing Fospice, and fully intend to always have a 'Fospice' dog in my home."

Foster Dogs, Inc. relies on donations to make all of their good work happen — and honored one benefactor in a special way. In 2018, the program was named "Chloe's Fospice Friends" to honor the memory of one of its biggest supporters and advocates — the late Chloe Kardoggian and her owner.

While the program has already done so much good in the New York area, Brasky said she hopes the idea will spread nationwide to help the dogs that are so often overlooked due to age or medical condition. She encourages adopters to consider pup who may not have much "time" left.

Approximately 3.3 million dogs enter animal shelters in the U.S. each year and about 670,000 of those dogs are euthanized, according to the ASPCA. Senior dogs, are adopted from shelters at less than half the rate of younger pups, according to research by the ASPCA.

"It's never enough time. Even if you have a dog from a puppy and you have them through old age. When is it, 'okay, I'm done. I'm good with this dog.' No, you want that dog forever. So, what we tell people is you're saving a dog…you're doing something that not everybody wants to do. And the dog is so grateful to you."