Your skin does not generally develop a dependency on everyday skincare products. However, products such as moisturisers help prevent water loss and keep your skin soft and comfortable. When you stop using them, dryness or tightness may become more noticeable, especially if your skin is naturally dry.
Some active ingredients can also influence how your skin looks and feels over time. For example, retinoids may help improve acne and skin texture with consistent use, but their benefits may gradually diminish when you discontinue them. This does not mean your skin has become addicted; it simply means the product was helping address a particular concern.