Yo cannot reference two different tables in a foreign key, so the relationship in the scenario will not be defined in the database. To make it work at all you would need to add [payer_from_table] and [payer_to_table] fields do differentiate between the two. If client #101 is "Moe's Tavern" in clientA but it's "Bob's Burgers" in clientB, you have no way to distinguish between them unless you specify the source table, too.
Another possible solution is to add a GUID [guid_id] field to both tables, which should create a unique identifier for every record regardless of table, assuming the tables are in the same database. You still cannot define a foreign key to two tables at once, but you can index the [guid_id] field in each table to keep it performant. You will not have things like cascading deletes unless you code them yourself.
A third option, which works with either scenario, is to create a third table that is periodically updated with data from both client tables. You would still need either a table identifier or a GUID so they can coexist. Your foreign key could then be defined against the combined table, with a complex key in the first case and against the GUID in the second case.