What is happening with 35mm film after expiration date? Will the ISO drop, so for example 200 ISO film one year after expiration date will be at an equivalent ~100 ISO?
Each light sensitive silver salt crystal that comprises film emulsion has an exposure threshold. We are talking about the amount of light energy required to render any given crystal developable. The ISO for any given material is an average of the communal sensitivities. The threshold value is variable. It is alterable due to the activity of the developer and a dozen other factors.
As time goes by, outside forces such as heat, pressure, ionizing radiation and chemical instability shove the crystal towards its threshold. Another way to say this, films and photo papers are constantly being fogged. In time, the material becomes useless as it will develop up just as if it had been exposed to light.
Now many fast films are hyposensitized at the factory. Suppose a recipe produces 400 ISO film. The maker might hyposensitize some and make a batch that is1600 ISO. This is done by chemical treatment or a controlled fogging to light or other radiation. Astronomers routinely treated film by baking in a container filled with a mixture of different gasses.
What I am trying to say is; aging film will boost its ISO. The problem is, aged film is unpredictable. It may be fogged beyond hyposensitized thus to overcome the fog, you must give the material more exposure. Also, be aware, color films contain multiple emulsion layers; these are independent as to the way they age. Thus color film undergoes a color balance shift as it ages.
At the very basics, that depends on how it was stored. let's say it was stored dry and frozen (best) conditions: It will take good quality pictures for many years, or even decades, past the expiration date. But if it was warm and humid, then it would take washed-out and grainy pictures.