In this paper, we propose Joint Latch (JLatch) and Joint Flip-Flop (JFF), two novel reconfigurable structures which bring the reconfigurability of reliability to user latches and flip-flops (FFs) in reconfigurable devices such as FPGAs. Specifically, we implement two reconfigurable storage elements that exploit a trade-off between reliability and amount of available resources. In fault prone conditions, JLatch (or JFF) is configured in such a way that four pre-selected normal static latches (or FFs) are combined together at circuit level to form one hardened storage cell. Solution focuses on transient faults such as soft errors, where we show that critical charge is increased by at least three orders of magnitude (1000X) to practically bring immunity against any Single Event Upset (SEU). If four latches inside an FPGA logic block are far enough, it can effectively cope with Multiple Bit Upsets (MBUs) as well. Additionally, provided that special transistor sizing is applied (only necessary for some latch structures), JLatch and JFF take advantage of a novel self-correcting technique to correct any single fault immediately. Our solution provides reconfigurability of reliability with negligible performance and area overhead with only one (two) extra transistor(s) per latch (FF). The delay of this technique is less than the delay of conventional TMR (Triple Modular Redundancy) technique with a majority voter at output.