Developers, fixers, and virtually all chemical products commonly used in film photography (or not) are prone to expiry over time. Nevertheless it is not uncommon to use expired chemicals in the hope that they might still work, as well as just for testing purposes.
What happens to film when it is developed using a chemical that supposedly expired? Does the film get damaged? Or does the developer simply fail to reveal the latent image?
It depends how far past the expiry it is, and how it's been stored. Different types of developers also degrade at different rates. Some developers will work just fine for years after their expiry date, others may be completely useless after a few months.
The first noticeable difference would be in the development time. Old developer will take longer, so you would need to experiment to figure out the required development times.
Once a developer gets completely past it though, you just won't be able to get a decent image from it, no matter how long you develop for.
If you under-develop the film because you've used an old developer and haven't compensated for this with longer development time, then there's nothing you can do about it. After fixing, you can't go back and give it another go in the developer. Your negative will be thin, and you won't be able to get decent contrast in the final print.
Having said all that, it'll either work properly or it won't. If after some experimentation you find your developer is still giving you a good image, then it's fine. You don't need to worry that it's past it's official expiry. It won't cause your negatives to degrade faster or anything like that.
To improve the lifespan of your film chemicals. You should...
Unless you don't care about your photos, it's a false economy to mess with expired chemicals, unless you do a clip test immediately prior to your intended processing.
