You should be able to delete fields with out deleting the referencing layouts. The fields will just disappear from those layouts. Relationships, scripts that reference the fields and calculation fields that refer to the field you are deleting are another matter. I jumped from 5.5 to 10, but assume 9 didn't change behaviour in this area. You should get warning messages when you attempt to delete a field used in a relationship or a script but still be able to delete the field. If a calcualation refers to the field, you should get a message identifying the referencing calculation field and you will be prevented from deleting the field until the referencing calculation field is either edited or deleted. As filemaker stops and reports on the first such referencing calculation only, it can be very tedious deleting a field that is referenced by a large number of calc fields.
Getting a copy of FMP adv and making careful use of its Database Design Report makes this kind of "prune out the dead wood" job a lot easier. (While upgrading from 5.5 to 10, I was able to use the DDR to identify and remove hundreds of fields that were no longer used.)
Hmm, I smell a database normalization problem. If I understand correctly, you actually have fields created in the database to store information for different years? Now that you are using FM9, there is a much better way to do this - really, the right way.
Create a table that contains the information you want to store for the year. Add a field that you can use to specify which year the data pertains to. Link this to the previous table by your 'key' field. Now, when you want to remove data from previous years, you just delete records.