This postcard was published in the Soviet Union in 1974. In that year, with Nikolai Podgorny as head of state, the Soviets conducted 21 underground nuclear tests1, launched a military space station, and saw the domestic release of the motion picture The Red Snowball Tree.
In this illustration, there is a small wooden house with a mother pig and several piglets inside. Standing outside are what appear to be husband-and-wife cats, carrying a broom and a small bag.
The Russian-language caption is as follows:
Ты впусти меня, свинья,
Я осталась без жилья.
Буду мыть тебе посуду,
Поросят качать я буду.
My best guess at the translation, with the help of Google as always, is:
You let me in, pig,
I was left without shelter.
I will wash your dishes,
I will rock your piglets.
(That's rock, as in "rock to sleep," I believe.)
From a cultural perspective, I'm not sure if there's supposed to be anything humorous about this. Or perhaps we're just supposed to take it as a straightforward tale of the poor offering their services to the middle class in exchange for basic life necessities.
P.S. — Did you notice that the roof seems to have a pig tail in the back?
1. The United States was also conducting numerous nuclear tests in 1974, of course, under Operation Arbor and Operation Bedrock.