Missing replacemente by a loop - Python

i have the following dataframe

id  value  year    audit     
 1     21  2007      NaN         
 1     36  2008     2011   
 1      7  2009      Nan  
 2     44  2007      NaN         
 2     41  2008      Nan   
 2     15  2009      Nan  
 3     51  2007      NaN         
 3     15  2008     2011  
 3     51  2009      Nan  
 4     10  2007      NaN        
 4     12  2008      Nan  
 4     24  2009     2011  
 5     30  2007     2011        
 5     35  2008      Nan   
 5    122  2009      Nan  

Basically, I want to create another variable audit2 where all the cells are 2011, if at least one audit is 2011, for each id.

I tried to put an if-statement inside a loop, but I cannot get any results

I would like to get this new dataframe

id  value  year    audit    audit2
 1     21  2007      NaN      2011   
 1     36  2008     2011      2011   
 1      7  2009      Nan      2011   
 2     44  2007      NaN      NaN            
 2     41  2008      Nan      NaN         
 2     15  2009      Nan      NaN         
 3     51  2007      NaN      2011      
 3     15  2008     2011      2011   
 3     51  2009      Nan      2011   
 4     10  2007      NaN      2011     
 4     12  2008      Nan      2011   
 4     24  2009     2011      2011   
 5     30  2007     2011      2011     
 5     35  2008      Nan      2011   
 5    122  2009      Nan      2011   

Could you help me please?