Your explode/implode idea isn't a bad one, I've used that technique many times in specific situations...but it gets messy, and you don't have to do quite that much work in this case (unless you want to).
Essentially what we're discussing is called "database normalization." One of the better essays I've read on the subject is actually on this site, posted back in 2000. I'll link it, although it looks like some of his diagrams aren't showing up right. It's this one. I'll summarize the most relevant points for this situation.
The general idea behind it is to make the table structure as general as humanly possible and eliminate any duplicated data. Anytime you're thinking about columns that could be called X, Y, A1, B1, C1, A2, B2, C2 then you could use some normalization. It would be much simpler to just say X, Y, A, B, C and then store 2 rows instead. Easier to search, easier to put data in and take it out, and more importantly you don't have to alter table structure if you need A3, B3, C3...just add another row. The problem you're pointing out is that the X column has to be unique (like your SSN field). (You're also duplicating data in the Y field, but the same solution fixes both of these things.)
The answer is to create your own internal id number for each person...this is exactly what Roger Ramjet is suggesting. An internal id would be unique to each SSN, but could show up as many times as needed in a secondary table because it doesn't really mean anything...except to point to the unique SSN. The idea is to have two tables...one that contains X and Y (the fields that are either unique or only show up once per person) and one that contains fields that might show up many times for a person. The internal id would be an auto-incrementing field on the X and Y table...and use that as a reference number in a field in the other table. So for example you might have (hopefully this diagram will work out):
X Y ID
--------------------------------------
111-111-1111 | Bob | 1
444-444-4444 | Jim | 2
A B C ID
---------------------------------------------------------------------------------------------
Blockbuster Montana 10 months 1
McDonalds Arkansas 5 months 1
Sears Arkansas 6 months 1
Goodyear Maryland 1 month 2
Now you can have as many employer rows for Bob as you need...just give the ID of 1 and you have a link between the information. Normalization is something I've always felt was dead simple once you see a few diagrams...and yet it can have a HUGE impact on your database design. It can simplify almost any project, small or large. One of my larger pet projects dropped from 20+ tables to 8 after I normalized everything properly, and in turn that greatly reduces the PHP needed to get all of that data. You can link the data together with SQL joins or with the PHP instead (using multiple queries) depending on your level of comfort with those two options.
I hope this didn't get too wordy and sheds a bit more light on one way to tackle the issue.