Table with two foreign keys pointing to the same column of another table

Yes it's perfectly possible to have 2 FKs each pointing to the same field of another table. I'd say it's unusual, and might be a symptom of a design that's not properly normalised. Consider

Every case has two clients

I suspect is an over-simplification. Are these two clients in distinct roles wrt the case? Even if there are exactly 2 clients for a fully-fledged case, maybe you only find out about them one by one? (So you first want to record the case, then later add party1, later again add party2.) Is it possible the two parties are the same client?

A more common design, as @AndreasT hints at, would be:

client table:  -- as you have

case table:
----------------
PK: case_id
    other stuff about the case, start date, etc

party-case-role
----------------
PK: { case_id(FK case table)
    { party(FK client table client_id)
    { role

where the role could be party1, party2, witness, consulted_expert, guardian, carer, ... (depending on what your cases are about)

This style of data structure is sometines called 'ppr' - person-party-role, and is common in industries with many cross-links amongst the clients/customers/suppliers/agents you're dealing with - in insurance or legal cases, for example.

For a query to return party1, party2 joined up with the case details (per your comment request) (untested)

SELECT case.*, p1.first_name, p1.last_name, p2.first_name, p2.last_name
FROM case
INNER JOIN (SELECT * FROM party-case-role WHERE role = 'party1' AS ppr1)
        ON case.case_id = ppr1.case_id
INNER JOIN client AS p1 ON ppr1.party = p1.client_id
INNER JOIN (SELECT * from party-case-role WHERE role = 'party2' AS ppr2)
        ON case.case_id = ppr2.case_id
INNER JOIN client AS p2 ON ppr2.party = p2.client_id