Hi, I have few employee's who have received Voluntary Attrition Packages back in July 2016 but the company wants to rehire these employee's only after 4 months of being laid off. Is there any implications to re-hiring employee's who have received their lump sum? Is there a time of how long an employee needs to wait until they are re-hired at the same employer? What are the legal issues with rehiring someone who took a severance package? Is the company required to offer employment to everyone that took the severance package? Can we extend an offer of employment to one and not all who took the severance package and left the company?

At least in the USA where I have worked you lose ALL previous time with company and any seniority after accepting a severance package if you are ever rehired for purposes of benefits etc..you are considered a new hire. You can offer it to anyone you wish and not to anyone you wish.

Actually been in this situation, or almost the identical one...Got laid off, paid severance and got called back 6 months later, only to quit less than a week later.

You need to consult your legal counsel. You need to read the Attrition package agreement carefully as it should spell out what happens in case of a re hire. While the normal thing is to have such a rehire start fresh the matter is up to company policy not statute. So the terms of the package is what is important here.

Aside from company policy, laws vary by country and by locale within the country.
In the US, there can be instances in which this could be considered a 'fake layoff,' which is illegal, but the details depend on several factors such as how many were let go.
On the other hand, since they received a lump sum, I don't think you can use the term layoff (which you did). Voluntary attrition is basically an enticement to QUIT, very different.
SO....
I suspect that it's all OK. But that's based on what you have said, and not knowing where you are.

What is your role? You say YOU have employees, but you don't know about company policy or the law.

I'm a HR generalist and I'm based in Canada. The reason I'm asking because my company doesn't have any policies in regards to the questions I asked (it's my 4th day at the job). My question was to gain some insight from other HR professionals that may have more knowledge in this area.

OK... were they laid off or not (did they file for unemployment)? How many left the company at the same time?

I'm not trying to be mean, but I suggest that you get some publications from the gov't, province and country, regarding labor laws, and study them, before you call yourself an HR professional. If your last job was as in HR in a big company, but doing one small part of HR, then you are in over your head, and the company could be sued. I don't even know what it means to be an HR generalist. A generalist in other fields means you know all of it.

As I said, this should have been spelled out in the agreement, Have you read it?

I have a feeling there wasn't one. Small company. Been there.