In this case the synonym should be properly deleted, if not, it cannot be used but still exists on sys.synonyms catalog.

You can check it running next script:

    IF OBJECT_ID('T1') IS NOT NULL
        DROP TABLE T1;
    GO
    
    IF OBJECT_ID('NEW_T1') IS NOT NULL
        DROP SYNONYM NEW_T1;
    GO
    
    CREATE TABLE T1(f1 int);
    GO
    
    INSERT INTO T1 VALUES (1),(2),(3);
    GO
    
    CREATE SYNONYM NEW_T1 FOR T1;
    GO
    
    SELECT * FROM NEW_T1;
    GO

    f1
    -----------
    1
    2
    3

    DROP TABLE T1;
    GO

    SELECT * FROM NEW_T1;
    GO

    Msg 5313, Level 16, State 1, Line 23
    Synonym 'NEW_T1' references an invalid object.

    SELECT name, object_id FROM sys.synonyms WHERE name = 'NEW_T1';
    GO

    name        object_id
    ------      --------------
    NEW_T1      1463676262

    
    IF OBJECT_ID('NEW_T1') IS NOT NULL
        DROP SYNONYM NEW_T1;
    GO