Inside the layer parameters, define custom resolution for zoom greater than 19. As in this case i have defined the resolutions till zoom level 22.
map = new OpenLayers.Map("osm");
var layer_osm = new OpenLayers.Layer.OSM(null, null, {
resolutions: [156543.03390625, 78271.516953125, 39135.7584765625,
19567.87923828125, 9783.939619140625, 4891.9698095703125,
2445.9849047851562, 1222.9924523925781, 611.4962261962891,
305.74811309814453, 152.87405654907226, 76.43702827453613,
38.218514137268066, 19.109257068634033, 9.554628534317017,
4.777314267158508, 2.388657133579254, 1.194328566789627,
0.5971642833948135, 0.25, 0.1, 0.05],
serverResolutions: [156543.03390625, 78271.516953125,39135.7584765625,
19567.87923828125, 9783.939619140625,
4891.9698095703125, 2445.9849047851562,
1222.9924523925781, 611.4962261962891,
305.74811309814453, 152.87405654907226,
76.43702827453613, 38.218514137268066,
19.109257068634033, 9.554628534317017,
4.777314267158508, 2.388657133579254,
1.194328566789627, 0.5971642833948135],
transitionEffect: 'resize'
});
map.addLayer(layer_osm);
the above script will result in loading the osm tiles from last zoom level (i.e. zoom 19) and show the same tiles for every zoom greater than 19.