Is it true that female dogs can have a condition called "false pregnancy"?

Yes. Some female dogs (bitches) fail to go out of their heat cycles correctly. This causes a condition we call "false pregnancy". Even though the bitch may not have mated with a male dog, her body believes it is pregnant due to some incorrect hormonal stimulations that it is receiving.

False pregnancy occurs 60-80 days after the bitch was in heat, about the time a pregnant bitch would give birth. (Pregnancy in a dog lasts about 63 days.) A dog experiencing a false pregnancy may have some abdominal swelling and/or engorgement of the mammary glands which can be painful. In some cases the bitch will actually produce milk, make a nest, and even collect socks or toys and hold them against her breasts. Bitches undergoing false heats generally do not experience serious long-term problems since the behavior disappears when the circulating hormones return to their appropriate levels. However, some bitches may have a false pregnancy with each heat.

One of the advantages of spaying your dog is that you can eliminate the possibility of this condition occurring.