A "Notice of Dropping Party" is a procedural device under Florida Rules of Civil Procedure 1.250 which is attached below. It has to be brought by the adverse party. So, for example, if you are the party being sued (the "defendant") the party suing you (the "plaintiff") may choose to drop you from the case. If the statute of limitations has not run, the plaintiff may bring you back into the case at some point if he/she can establish good cause. Attorneys have various reasons - some strategic - for "dropping" parties as opposed to simply dismissing them from the case.
RULE 1.250. MISJOINDER AND NONJOINDER
(a) Misjoinder. Misjoinder of parties is not a
ground for dismissal of an action. Any claim against a
party may be severed and proceeded with separately.
(b) Dropping Parties. Parties may be dropped
by an adverse party in the manner provided for voluntary
dismissal in rule 1.420(a)(1) subject to the exception
stated in that rule. If notice of lis pendens has
been filed in the action against a party so dropped, the
notice of dismissal shall be recorded and cancels the
notice of lis pendens without the necessity of a court
order. Parties may be dropped by order of court on its
own initiative or the motion of any party at any stage
of the action on such terms as are just.
(c) Adding Parties. Parties may be added once as
a matter of course within the same time that pleadings
can be so amended under rule 1.190(a). If amendment
by leave of court or stipulation of the parties is permitted,
parties may be added in the amended pleading
without further order of court. Parties may be added
by order of court on its own initiative or on motion of
any party at any stage of the action and on such terms
as are just.