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The permit allows you to stay in the Schengen area during its period of validity.
If I didnβt have that permit card would I have had a big problem?
Yes. Without that card, the border officer has no way of knowing that you aren't a visitor. Without the card, the officer is supposed to determine whether you have complied with the limit of 90 days in every 180-day period allowed for visitors. Without the card, you would be subject to a fine or worse for overstaying this limit.
The card also exempts you from ETIAS.