Rescue and foster dogs can come with numerous behavioral issues to resolve. We have no idea what they have been through in their lifetime. People assume that an adult dog is house trained but this is often not the case with rescue and foster dogs. Even if they have basic house training, insecurity and a change in environment can cause them to have accidents. Do not punish this behavior but instead give them a clear sign of where they ARE suppose to go.
When a new dog enters your home it should be common practice to take the dog to this spot once every hour and praise them when they go. Never leave them unattended. Keep your dog on a regular feeding schedule and you will quickly be able to determine when they need to eliminate.
Your dog should always be given an opportunity to go first thing in the morning, last thing in the evening and before you leave them alone for any length of time, also upon your return.
Crate training is perfect for overnight and when you are at work however if you are dead set against using a crate our diapers are the answer. Our diapers are made to be lined with adult incontinence pads (Poise, Attends, etc.). Just remove and dispose of the pad. They are also machine washable for larger messes.
It is important for the success of house training that you only use a diaper when necessary during long periods of time away from your dog or overnight while sleeping.