I all depends on what kind of protein/enzyme you are working on.  Assuming the two more days in 4 C is still sterile and that the protein is there.  I would also do an enzyme assay to make sure that it's active before going down the purification process.

It's riskier that there will be proteolytic degradation or loss of enzyme activity, but you might get away with it. At the end, you will want to make sure the mass is correct and the enzyme activity is what you expect it to be. In the future, try to work through the whole protein prep as quickly as possible.

Agree with Adam.  At least get the cell pellet and store in -20C or colder.

Its better to get the cell pellet and store at -80C, and when you want to use the protein,lyse the cell that time and get the proteins. By this way, you can get the protein in active form. Do remember to use your protein as soon.

I agree with Zahir. I stored my samples (also BL21) at -20°C, for longer storage -80°C is better (more than 4 weeks). When you want to store your purified protein at 4°C maybe addition of protease inhibitor cocktail tablets is an option (for me it worked pretty well). Be careful with EDTA based tablets. EDTA could interferre with your activizy assay.

Thank you for your valuable information

I agree with the above answers. I used to cryo freeze the cell mass in Liquid nitrogen and store them at -80 C for longer use. I think it matters with the activity of Protease. Generally at 4 C, the Protease will be inactive but the activity of the peptide/protein might  differ. EDTA free PI tablets may do the work.

Purify and check the integrity of the protein by running it on SDS-PAGE & if you have an assay, check the activity.