Como dizer "pro cachorro não sair" em inglês

I like Juliana's answer.

I would suggest "to get out" (assuming the dog is still in an enclosed area - and that includes being out of the kennel but still in the yard or general area of the owner's house). Or "to get away" (it doesn't matter where the dog is). "To escape" is certainly possible, but personally I would not choose it. It implies that the dog was being held prisoner, kept against his will. And it sounds formal although clearly used in an informal setting.

"To shut" and "to close" have the same basic meaning. Shut the gate./Close the gate.

Here is what Merriam-Webster has to say about kennels:

1.
A (1) : a house for a dog or pack of hounds (2) : an establishment for the breeding or boarding of dogs — usually used in plural
B : a house or other dwelling place regarded as unfit for human residence

2.
A : a pack of dogs or other animals
B : a group of persons
<literary agent who has a kennel of eccentric clients — Martin Levin>

3.
A : a bed or den of an animal (as a fox or otter)

4.
A : gable 2b

I have never kept dogs in an enclosure, but I was surprised to read in M-W: "a house for a dog or pack of hounds". I call an fenced enclosure a "kennel" but a house for a dog is "a dog house".