I acquired a genuine background stand a number of years back; it was an ePrey purchase that I don't recollect as being a whole lot of money -- maybe a hundred bucks or so. It has two heavy duty adjustable uprights with tripod-like legs (think large heavy light stands) that can go up to 8 or 9 feet. There are four approximately 3 foot sections with fittings to slide together for a horizontal bar. The fittings allow setting up for 6, 9 or 12 feet of width. My wife stitched up a dark cloth with a buttonhole slit in the center and a pocket on one edge to slide onto the horizontal bar. This was all for a light baffle to stick the camera lens through and photograph paintings on site with very controlled light at some art shows I helped set up. I think it would be a fair amount of overkill for simple portraiture.
If I just wanted a three or four foot wide cloth hung vertically I might think about some creative super 'Tinker Toy' approach using 1 or 1-1/4 inch plastic pipe. I expect one could leave a few of the fittings uncemented so the frame could be slid apart for travel and storage. As I have the aforementioned alumin(i)um stand, I haven't given it much further thought. The plastic pipe is pretty cheap, the fittings a little less so, depending on which ones are needed. Many fabric stores have cloth in 36 to 54 inch or so widths that can be bought by the yard. There's a huge array of colors, textures, etc. that are not generally very expensive unless you get into exotic patterns and materials (which you'd not likely need for a backdrop).