How does the NFL prevent a team on the last week of the season to losing on purpose ensuring a #1 draft pick for the following year?
This isn't the reason but a reason: Player Incentives.
Late in the season, players are close to reaching incentives that would reward them in bonus money if they were to reach said incentives. This provides an incentive to be productive, even if the team is also in a spot to get the #1 pick in the draft.
Now, that doesn't stop a team effort from tanking. However, players may rebel at such a notion. An example of this is Doug Pederson and the Philadelphia Eagles at the end of 2020. The Eagles were out of playoff contention and lost to the Football Team.
I'm not sure prevention is necessary. Generally at the end of the year you have two or three teams in a "race to the bottom". But such teams have a strong motivation not to lose:
- Teams are very competitive by nature. No one enjoys losing.
- Coaches with poorly-performing teams risk being fired. Winning improves their prospects.
- For players in this injury-riddled sport, the earnings window is very short. They get paid, either by their current team or their next team, based on their on-field performance. Players play hard to show their value.
I have one data point which may illustrate. Gary Kubiak coached the Denver Broncos during the 2016-17 season. He had won the Superbowl coaching the Broncos in 2015-16. The Broncos were 8-7 heading into the final game of the 2016 season. They had been eliminated from the playoffs. Losing would have meant better draft picks the next Spring. The Broncos played their starters against the Raiders (who had playoff positioning at stake) and beat them 24-6.