In this case, 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 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