Honey and Racer - who are totally inseparable - were surrendered after their owner died.
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Racer has three legs but gets by very well, according to staff.
The duo would do well in a home with a big yard.
"They've spent two years in a kennel with playtime yard access so a home with a yard, even if walks are limited, would be an upgrade for them," read a post published on the Burbank Animal Shelter's Facebook page.
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After so much time, staff hopes the "pair of imperfect pups" can finally find a loving home.
"We're just looking for a home that's going to spend a little bit of time with them and love them," said Stacie Wood-Levin, a senior animal control officer for the city of Burbank. "They would be perfect for maybe someone that's retired. They don't have to be in the house all the time, they actually enjoy being in the yard. They're just kind of mellow, chill dogs."
If you're interested in adopting Honey and Racer, contact the Burbank Animal Shelter at 818-238-3340.