to the dogs

throw to the dogs AND
give to the dogs
выбросить за негодностью, за ненадобностью; бросить на произвол судьбы

Example: She knew that when keeping her on got too hot for him Jim would throw her to the dogs. — Кит знала, что, если ее присутствие окажется слишком опасным, Джим не задумываясь пошлет ее ко всем чертям. (Sh. Anderson, "Kit Brandon")

go to the dogs — катиться в пропасть; || пойти псу под хвост, пойти коту под хвост; впустую, (все) напрасно

Example 1: This country is going to the dogs. — Страна катится в пропасть.

Example 2: My whole life seems to be going to the dogs. — Вся моя жизнь, кажется, пошла псу под хвост.

Related vocabulary:
[down the drain]
out (of) the window (gone, wasted, or no longer in existence)

Example 1: All that work gone out the window because my computer crashed.
My forty dollars—out the window! Why didn't I save my money?
(Cambridge Idioms Dictionary)
Example 2: It is as if everyone's good judgment has flown out the window.(thefreedictionary.com)
Example 3: If we quit now, we might as well just toss three months' work out the window. (thefreedictionary.com)

go/fly out (of) the window
if a quality, principle, or idea goes out of the window, it does not exist any more

Example 1: Then people start drinking and sense goes out of the window. (Cambridge Idioms Dictionary)