When someone worries more about losing what they have than gaining something new, what psychological bias is at play?

The psychological bias at play is Loss Aversion. Loss Aversion is a cognitive bias describing the tendency for individuals to strongly prefer avoiding losses over acquiring equivalent gains. It means that the psychological impact or pain of losing something is subjectively felt as more intense than the pleasure or utility derived from gaining an equivalent item or amount. This concept was famously identified and incorporated into Prospect Theory by psychologists Daniel Kahneman and Amos Tversky. Prospect Theory's value function illustrates this by showing that the curve for losses is significantly steeper than the curve for gains, meaning that a given loss feels much worse than an equivalent gain feels good. For instance, the negative feeling associated with losing $100 is typically more potent than the positive feeling associated with gaining $100. Consequently, when someone worries more about losing what they already possess compared to the potential benefit of acquiring something new, they are demonstrating Loss Aversion, as the perceived disutility of the potential loss outweighs the perceived utility of the potential gain.