It never hurts to email or otherwise ask.

Them accepting is not sure and will vary greatly depending on the person. A digital image is highly valuable, so if the person taking the photo is a professional or someone interesting in photography business, they will be reluctant to offer it for free. Prints are most likely to be sold because a perfect copy or enlargement is harder to make. Although in this day and age, digital files are frequently being licensed.

The image is their property and if they trust you, some people may simply decide send you a digital file on the understanding that it will be for your personal one-time use. I know professional photographers who allow this for watermarked images.

A digital photograph these days is rarely sold but licensed. The photographer remains the owner and you get a licence to use it for a particular use. This determines the price of a licence. Since you are asking for single-time-use in private home, you are likely to get one of the lowest price. What that price is though, is entirely dependent on the photographer.

Now many images on the web are produced by non-professionals who are not interested in making money from images and those people are most likely to accept sending a high-resolution version.