Foreign Key - One Child Table to Multiple Parent Tables
I'm not sure I've seen any DBMS support multiple parents for foreign keys like this, it is probably assumed that something needed this is not in good form (the linking field is explicitly overloaded as it can refer to several distinct types of thing, which means it dos not fit an accepted "normal form").

You could instead have a general "AccessableThings" table that contained just the IDs, and then have the UserItems/SystemItems/OtherItems/etc refer to that via FK (to ensure everything in those tables also appears in the IDs table) as well as AccessControl doing so. If you have other generic fields that apply to all types ("display name" for instance) then you might include them in the AccessibleThings table to so you can avoid joining in all the other tables when all you need are generic details.

CompanyItems            AccessibleThings          AccessControl
============            ================          =============
CompanyID PK FK ------&gt; ThingID PK      &lt;--.      AccessRuleID PK
&lt;companyfields&gt;   |     &lt;genericfields&gt;    |----- ThingID FK
                  |                               &lt;AccessRuleFields&gt;
SystemFiles       |
===========       |
FileID PK FK -----|
&lt;filefields&gt;      |
                  |
SomethingElse     |
=============     |
SomethingID ------|


This will enforce things being correct as entered, though can not delete AccessControl on the delete of an Item, just on delete of the AccessibleThings row (which can also cascade to the Items tables of course) so this table becomes the central object in that regard. Obviously your data access layer (or business logic, but the data layer is more likely the correct place) will need to know about the new structure at each relevant point.

Alternative:

You could also enforce your more complex data integrity relationship entirely via triggers, though you need to be very careful with both complexity and efficiency here otherwise you could create a veritable zoo of nightmares for later.