If they have a pre-2009 divorce decree, see Pub 501 for the rules. It may be possible to attach some of the pages of the decree to the 1040 and claim an exemption for the child.  I personally have never seen a decree that met the IRS requirements.

If they have a post-2008 divorce decree, your client may not file a return claiming the child without the signed 8332. The IRS does not care what the divorce decree says. Your client should file a return now (because it is already delinquent) that does not claim the child.

Your client can take the ex to court to compel them to sign the 8332 (and I'd be sure to get a signature specifying the future years, as well). At that point, your client can amend to claim the child. Your client's lawyer should be able to advise as to whether they'd have a claim for the additional legal fees and cost to amend.

For children who have attained the age of majority, there's a good argument to be made that the divorce decree is no longer controlling, that an 8332 isn't effective, and that the general IRS dependency rules are the only determinative factor.