It do not know if that's a good design practice but for sure it is possible to have a composite foreign key of one table that is the part of the composite primary key of other table.
Say we have a table test1 having a composite primary key (A, B)
Now we can have a table say test2 having primary key (P, Q, R) where in (P,Q) of test2 referencing (A,B) of test2.
I ran the following script in the MySql database and it works just fine.
CREATE TABLE `test1` (
`A` INT NOT NULL,
`B` VARCHAR(2) NOT NULL,
`C` DATETIME NULL,
`D` VARCHAR(45) NULL,
PRIMARY KEY (`A`, `B`));
CREATE TABLE `test2` (
`P` INT NOT NULL,
`Q` VARCHAR(2) NOT NULL,
`R` INT NOT NULL,
`S` DATETIME NULL,
`T` VARCHAR(8) NULL,
PRIMARY KEY (`P`, `Q`, `R`),
INDEX `PQ_idx` (`P`,`Q` ASC),
CONSTRAINT `PQ`
FOREIGN KEY (`P`, `Q`)
REFERENCES `test1` (`A`,`B`)
ON DELETE CASCADE
ON UPDATE CASCADE);
In the above mentioned case, the database is expecting the combination of (A,B) to be unique and it is, being a primary key in test1 table.
But if you try to do something like following, the script would fail. The database would not let you create the test2 table.
CREATE TABLE `test2` (
`P` INT NOT NULL,
`Q` VARCHAR(2) NULL,
`R` DATETIME NULL,
`S` VARCHAR(8) NULL,
`T` VARCHAR(45) NULL,
INDEX `P_idx` (`P` ASC),
INDEX `Q_idx` (`Q` ASC),
CONSTRAINT `P`
FOREIGN KEY (`P`)
REFERENCES `test1` (`A`)
ON DELETE CASCADE
ON UPDATE CASCADE,
CONSTRAINT `Q`
FOREIGN KEY (`Q`)
REFERENCES `test1` (`B`)
ON DELETE CASCADE
ON UPDATE CASCADE);
In the above mentioned case database would expect the column A to be unique individually and the same follows for column B. It does not matter if combination of (A,B) is unique.