A triggered stop becomes a market order, and market orders pay whatever the book offers. In a liquid stock at midday that is a cent; in the same stock on an earnings gap it can be dollars.
The asymmetry is the point. Slippage on a stop is one-directional by construction - you are selling into falling liquidity or buying into rising prices, always alongside everyone else with the same level. Measure it: record planned exit versus filled exit for every stopped trade and you will typically find real losses run 5-20% larger than planned in liquid names and far more outside them.
Budget for it rather than being annoyed by it. If your average stop slippage is 8%, your 1% risk rule is really a 1.08% rule, and your expectancy calculation should use realised exits, not planned ones. See slippage-budget.
Related: slippage-budget, slippage, hard-stop, worst-case-loss