Can you play Safety Inspector on a battlefield where you have one unit in your turn, and then kill that unit on the battlefield?

Yes, you can play Safety Inspector on a battlefield where you have one unit, and you can kill that unit as part of the resolution of Safety Inspector's "When you play me" triggered ability.

1. Playing Safety Inspector

• Step 1: You declare playing Safety Inspector from your hand to a battlefield you control.
• Step 2: You choose whether to pay the optional additional cost of 3 XP.
• Step 3 & 4: You pay the total cost (5 Energy, 1 Power, plus the 3 XP if you chose to pay it). Safety Inspector then enters the chain (Rule 737.6).

2. Resolution of the "When you play me" ability

Once Safety Inspector enters play, its triggered ability ("When you play me, each player must kill one of their units") is placed on the chain.

• If you paid the 3 XP cost: The ability states, "If you paid my additional cost, you don't kill a unit this way." Therefore, you are not required to kill your unit. Your opponent, however, must still kill one of their units if they have one at that location.
• If you did not pay the 3 XP cost: You must resolve the ability as written: "each player must kill one of their units." You are required to kill one of your units. Since you have one unit at that battlefield, you can choose to kill it to satisfy this requirement.

Regarding Battlefield Control

Because Safety Inspector is an item on the chain, you will not lose control of the battlefield when you kill your unit (see Rules FAQ Clarification 2026-04-29). Even if that was your only unit at the battlefield, the presence of the ability on the chain protects your control of that location until the ability finishes resolving.

Note: I could not fully verify this ruling against the retrieved rules.