Are there any dogs can live with open fenced garden?

[quickname]

I rent a cottage on an arable farm, with a large garden but the fencing is completely open.
There are many rabbits/ hares/ pheasants/ partridges sometimes even a deer pass close by or even directly in the garden.

I would love to home a smallish older dog, based on the dogs of friends I've met who I could see would fit our lifestyle and also of course would be nice to give a home to an older dog that others might not want. We used to have staffies many years ago but whilst they were besotted with their humans they couldn't help themselves and chased any creature that moved. So I know they would never have been able to live in a house like this.

But do all dogs require a secure garden? Are there any breeds who preferring lazing in a garden with no desire to run free across fields?

Any dog that would be in that situation would need you to be constantly out in the garden with it, it's not something to risk!

yes, they all have instinct of following scent so you will run a risk of dog walking away to follow interesting scent
most IMHO would chase any moving wild animals as well

Could you put wire fencing up on the inside of the open wooden fencing to contain the dog?

My garden is somewhat similar and I put a fenced in dog area out the back. I don't think there is any dogs who absolutely won't follow a scent and it's really not worth the risk.

Could you fence an area adjacent to the back door? I would have kittens letting a dog out into an unfenced garden. In a rural area could be a problem with livestock too.

Oh, sorry see you said arable farm, so no livestock, just wildlife!

Could you put wire fencing up on the inside of the open wooden fencing to contain the dog?

^^ This.

Doesn't have the be an inner fence, just wire mesh stapled to your side of the fence?

I spoke to the landlord today but he is completely anti dog! had not expected that and insists we cannot have a dog here sooo sad