LDO that doesn't drop out?
Most LDOs do similar to what you describe except that when the input goes below the programed Vout + dropout, 7V in your case, the output continues to be the input minus the dropout voltage.
The dropout of the UCC283 at 1.5A output is typically 200mV so at 7V input the output voltage would be 6.8V.
If you want to reclaim that last 200mV you would need a mechanism to bypass the regulator altogether. You could then have the problem that @Elliot Anderson describes in the comments where the output could jump between the two voltages in an undesirable fashion.
There are buck-boost switching regulators that can do what you describe - they either step down or can step-up when the input is too low.
In one case I implemented a system with a boost converter to provide 6V to an LDO configured to provide 5V. At input levels above 6V the boost converter would pass through with a diodes drop and as the voltage went below 6V it would start boosting. At all times the LDO would have at least 6V input and so could reliably provide 5V output whether the input voltage was 3V or 9V.