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Which phone are you using? Are you syncing contacts to your phone from a cloud account (Google, Microsoft, iCloud, etc.)? If so, then they'll be deleted from the cloud account when you delete them from the phone. They'll only be deleted from your phone's local storage (or its SIM card) if that's where they're stored in the first place.
I'm using a Samsung Galaxy S9, and this is how I configure the Contacts app to show me only the contacts from my primary cloud account:
Open the Settings menu, then tap "Settings->Contacts to show." The following list appears:
All contacts (displays all contacts regardless of whether they're stored locally or synced with a cloud account)
Phone (displays only locally-stored contacts)
SIM card
Samsung account
CardDAV
Custom list (with a little gear icon to the right that allows me to configure a combination of the above)
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