You can add Time to a Pay Per Ride metrocard. The vending machine will prompt you to choose. You can also tell the agent to add Time to your metrocard if you're paying at a booth.
Once Time is added, the metrocard behaves as an unlimited metrocard until said time expires. After that, it will behave as a "Pay Per Ride" metrocard again. You can refill a metrocard with either Time or Value (money) as often as you'd like. Source here, relevant example (copied from source) pasted below:
For example, if you have $5 in value remaining on your MetroCard and
add a 7-day unlimited ride pass, the next time you use your card, it
will activate the unlimited rides and the $5 value will only become
available when the 7-day time period expires. Note again however, that
if a customer wants to access locations where a 30-Day pass is not
accepted such as express buses, PATH or AirTrain stations, the
appropriate fare will be deducted, as long as there is enough monetary
value on the card.
Metrocards usually expire after a year:
Has your MetroCard expired?
Whether Pay-Per-Ride or Unlimited Ride, every MetroCard has an
expiration date. The date is located at the upper left corner on the
back of the card. The expiration date is usually about one year from
the date of purchase.
If your Pay-Per-Ride MetroCard expires, you have two years from the
expiration date to transfer any remaining money to a new card. Within
the first year after expiration, bring your expired card to any subway
station and ask the agent to make the transfer. After that time, the
expired MetroCard must be sent to MetroCard customer claims. Ask the
station agent for a postage-paid Business Reply Envelope.
MetroCard Customer Claims
130 Livingston Street
Brooklyn, NY 11201