If you are extensively scouting countries, you can find great prospects available as Unrestricted Free Agents. They are always appearing first at the end of the fourth season.

Here is the explanation of what we can call a bug of EHM :

The main reason is a dysfunction in the computer generation of the draft players. Some players generated shouldn't be there.
In the real NHL, players eligible to an NHL draft (except over agers) should be 18 years old, before the 1st october of the draft year. For example, players eligible to the 2003 draft must be born before the 01/10/85. All guys born after this date will be eligible to the next draft. This feature isn't included in EHM so you can find players born in october, november and december. This would have been a minor problem if it haven't resulted in a major bug.

The best to understand the problem is a concrete example :

1st october 2002 : Start of the first season. EHM generates the first draft players. Now let's take the case of a specific player : Scott Leach, born : 11/12/85.
Age : 16 years old - Contract : undrafted
June 2003 : The draft. Anaheim selects Scott Leach and signed him to a 3 years contract.
Age : 17 years old - Contract : 3 years
1st october 2003 : End of training camp. Scott is returned to juniors.
Age : 17 years old - Contract : 3 years
End of june 2004 : End of the first year of contract.
Age : 18 years old - Contract : 2 years
1st october 2004 : End of training camp. Scott is returned to juniors.
Age : 18 years old - Contract : 2 years
End of june 2005 : End of the second year of contract.
Age : 19 years old - Contract : 1 years
1st october 2005 : End of training camp. Scott is returned to juniors because he is too young to play in the minors. You can notice that if the draft rule would have been respected (born before 1st october), he would have been able to play in the minors.
Age : 19 years old - Contract : 1 years
June 2006 : Players returns from juniors. Scott's contract is ending in one week.
Age : 20 years old - Contract : 1 week (RFA status)

Here comes the first bug. Computer AI seems to check RFAs in the pro and farm team but not in the juniors. So the game will never give the qualifying offer during the regular season.

21th june 2005 : End of the third year of contract. The Computer AI hasn't made a qualifying offer, Scott is becoming an UFA.
Age : 20 years old - Contract : UFA

Here comes the second bug. During this week, the AI won't sign the prospects RFA. Why ? I don't know. Perhaps because All RFA players are expected to be signed at this time.

There is only one way to solve this problem. Take control of each team and give the qualifying offer to every prospects in this case before they are released to free-agency.