Writ. An order issued by a court requiring that something be done or giving authority to do a specified act.

Therefore, should the defendant fail to show or to challenge the complaint by the defendant, the court makes the petition into a collection instrument.

I would therefore simply translate it as follows:
..., sob pena de se constituir de pleno direito o titulo executivo judicial, convertendo-se o mandado inicial em executivo.

..., the failure of which rightfully converts the initial writ into a judicial instrument of execution.