Priors are just statistical distributions that reflect the initial expectation that the modeler has about each parameter. The very first thing we need to decide is, what is the support for the corresponding distributions? For example, for most coefficients in a linear regression model, the modeler very likely knows the correct sign for them. When modeling sales of a product in terms of its price and a promotional effect, the price effect should be negative (a higher price = less sales), and the promotional effect should be positive (more promotion = more sales). It would be natural then, to assign a distribution, bounded by zero, to both parameters. Sometimes we don't have a clear idea, and in those cases it is advisable to choose a distribution that has a support between -∞ and ∞. In this fashion, we will be allowing the posterior density to take any value. Any restriction on the prior's support gets translated into the posterior's support (by support, we mean a range of permissible values).