We have performed experiments on model emulsions of polyisobutylene (PIB) and poly(dimethylsiloxane) (PDMS) to quantify the effect of confinement on deformation and stability under flow of droplets and strings (threads). It is known from earlier work from our group that, under confinement, droplets in concentrated emulsions can coalesce with each other and elongate in the flow direction to form stable strings. In the present context, strings can be simply viewed as droplets having a large aspect ratio whereas, in the bulk case, there are two known states of a droplet (stable and unstable), as determined by the droplet Capillary number (Ca). We find that confinement effects induce three additional states: squashed drops, stable strings, and unstable strings. For strings, deformation under confinement is a very strong function of Ca: the aspect ratio of a string scales nearly as Ca-3. This scaling relationship is unique to confinement, and it sets strings apart from transiently stretched droplets in the bulk. Confinement not only promotes deformation but also allows larger stable droplets to exist under flow than what is predicted by the critical Ca. Strings are stabilized by a combination of the shear flow field and wall effects arising from confinement.