The rental market in Sweden is limited, there are more people looking for rentals than landlords letting out properties.
When supply and demand are not aligned, a niche market can develop and that is what has happened in Sweden. Since taxation laws in Sweden entail that being a landlord is not financially advantageous, the investment properties are few and far in between. The typical rental property is owned by a family that is being moved abroad for an expat assignment and as a result are subletting their apartment or house.
Therefore, landlords can usually pick and choose to whom they rent to and large publicly noted companies are preferred. The reason for this is that many landlords in Sweden feel that a large corporate tenant is more secure than renting out to a private individual. So, what to do if your company will not sign the lease on your behalf? Ask them to sign a letter of guarantee of all rent and damages. This will increase your chances of being chosen. Those without a company to sign the lease or ability to produce a letter of guarantee unfortunately will not be as popular of a tenant.
Fret not though, if you come prepared and make a good impression you should still find a suitable home. You may not have as much to choose from as a private tenant per se but if you act quick and is amenable to the landlord you will find a home. Prepare a PDF of you and your family in order to bring a soft value appeal. Make it personal since that is what you have to work with if your company will not sign the lease.
A mistake we have seen many times is when those coming from abroad have not received an explanation of our market. When expectations are properly aligned, positive result usually ensue. Remember, your rental market or what you would get in your homeland is not relevant to the market you are entering. If you are searching as a private individual for a house in an "A" location such as Djursholm in Danderyd, you may have a choice of 2 houses vs. 5-7 as corporate tenant.