They kept monking.

Monks weren't ONLY scribes. Being an amanuenses, a scribe, was only one of the specializations a monk could have: some were farmers, others beggars, others blacksmiths, mathematicians, preachers, medics... some orders specialized in writing and decorate books, like the Carthusian, but even a Carthusian monastery was big and busy and needed more than scribes and librarians.

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Even before the invention of the printing press, monasteries hadn't the monoply of book production in Europe. Universities had their own scriptoria dedicated to copy books, and the University of Bologna was founded in 1088. Even privates could own their own scriptoria: Christine de Pizan was an Italo-French was a poetess, author and businesswoman that lived in late XIV century and paid people to copy her books.

Monasteries had lost the monoply on books much, much earlier than 1453.

When printing press come to be in late XV century, the monasteries adapted. For the latter half of XV century early printed books (incunabula) were similar to hand-made books, down to the miniatures: printers would hire an artist to decorate an miniate initials and margins. They sometimes were monks, sometimes laymen.

Some monastery embraced the new technology. Plenty of monks, mostly Benedectine, traveled from monastery to monastery becoming master printers and teaching the art to their brothers. In particular the Benedectine Monastery in Subiaco, near Rome, was home to Conrad Sweynheym and Arnold Pannartz, two german monks that learned their trade from Gutenberg's partners. The Subiaco printing mill is considered one of the first (if not THE first) printing laboratory in Italy, and its incunabula are considered among the most beautiful in the world.

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So... they adapted, like everyone else.