Can I play Cull the Weak and Safety Inspector with no other minions on board?

You can play Cull the Weak even if you control no units, and you can play Safety Inspector even if you control no other units.

Playing Cull the Weak

According to multiple RiftJudge FAQs (e.g., ID 8497, 1732, 2730), you can play Cull the Weak even if you do not control any units.

• Not a Target: The spell does not require you to choose a unit when it is played. The choice happens during resolution.
• "Do As Much As You Can": Rule 055 states that you follow instructions as much as possible. If you control no units, you simply do not kill one, while your opponent must still fulfill their part of the effect if they control any units.

Playing Safety Inspector

Safety Inspector is a unit card. According to the <chain_rules>, units entering play enter the chain, skip Execute/Pass, and resolve immediately.

• Playing with No Units: You do not need to control other units to play Safety Inspector. It is a standalone unit.
• Additional Cost: The ability "You may spend 3 XP as an additional cost to play me" is optional. You may choose not to pay this cost.
• "When you play me" Ability: This triggered ability uses the chain (<chain_rules>). When Safety Inspector enters play, this ability is placed on the chain.
  • Resolution: When the ability resolves, it instructs each player to kill one of their units. Because this is a triggered ability on a unit you just played, the "Do As Much As You Can" rule (Rule 055) applies here as well. If you control no other units (and assuming your opponent has units), you cannot kill a unit, so you ignore that part of the instruction.
  • If you paid the additional cost: The text "If you paid my additional cost, you don't kill a unit this way" provides you with an exemption from the effect regardless of whether you have a unit or not.

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