Once a month or so i bug out to the woods. Mainly so my 6 yo can make it to a place where i have supplies stored. He may be my life line at some point. Anywho we always build some type of shelter and fire. We have had hard heavy rains recently. In fact it was pouring when we went yesterday. i tried everything under the sun to get a fire going. In fact i burned everything i had that was flammable in our bobs. O well better luck next time.
A small kindle bag with some birch bark, that you find on the ground wood shps etc.. can help with starting a fire.
In regard to finding famable material during rain, not going to work much unless you find a sheltered area such as making a wood pile that you put under a waterrestistant leanto.
However a simple popcan burner and a bottle of hard liqour should be enough to have the ability to cook and warm yourself.
Also if you have something to make wood strips you can chop wood in half and use the inner part of the wood for the fire discarding the water soaked part.
This while drying the damp/wet wood next to the fire.
In an emergency if you see a birch or like tree, you can go under the top layer. Birchbark is more or less waterproof so wood underit will be dry.
Pine and cedar branches also with the needle etc.. go up right easy and don't absorb water much. Even sap is flamable..