The executor must first look to the will to see whether there is anything in the will that would prevent this. For example, the house might be left to one of the beneficiaries as their inheritance, either outright or in a trust. Or the will might state that a certain beneficiary has a specific amount of time to come forward with an offer to purchase, during which time nobody else can buy it. This might happen if the deceased had felt that more than one of the children might be interested in the family home, or if there is something unique about the property, such as a farm or family cottage.
Another option, although a rare one, is that the deceased might have specifically directed that the estate be liquidated, possibly to prevent any of the beneficiaries from owning any particular property.
If the will doesn't specifically prevent the executor from selling to a family member, the executor can go ahead and arrange to sell the property to the family member. It must be sold at fair market value, in other words, the price it would fetch if it were sold on the open market. (Executors would be well advised to protect themselves by gettiung two or three appraisals before agreeing on a price).
The executor must always remember that the beneficiaries can't receive anything from the estate until the deceased's debts have been paid, so it's possible that the house is needed for paying debts. In that case, the family member who wants the house is out of luck.
If the family member who wants to buy the house is a beneficiary, and the house is worth less than the beneficiary's total inheritance, the beneficiary can simply choose to take the house instead of cash. For example, the beneficiary's share of the estate might be worth $500,000, while the house is worth $400,000. Instead of taking $500,000 cash, the beneficiary might want to take the house plus $100,000.
If the beneficiary's share is less than the value of the house, the beneficiary may still use his or her inheritance to buy the house. For example, if the beneficiary's share is going to be $200,000, and the house is worth $400,000, obviously the beneficiary can't simply take the house. But he or she would only have to pay $200,000 for the house, as the other $200,000 is coming out of the estate.
Don't try this without the help of an estate lawyer!
One last thing that might cause a problem for the executor is a lack of powers and authorities in the will. This is a section of the will in which your estate planning lawyer examines your goals as stated in the will, and the assets you own, and includes the legal wording that will make sure your wishes are carried out in the most effective way possible. This is almost always missing from home-made wills, and frankly, sometimes even in the wills drawn up by non-specialist lawyer.
For example, in many jurisdictions, the law says that if an executor needs to sell the house from an estate to pay the bills, he doesn't need anyone's permission. However, if the executor is going to sell the house for any other reason - such as to sell to the beneficiary discussed in this post - he does need permission. He needs the written ok of all residuary beneficiaries. If one of those beneficiaries is a minor, the permission needs to come from the Office of the Public Trustee.
Having said that, the lawyer drawing the will should have included a clause that dispensed with the otherwise needed permission.