Foreign key default value
I'm not sure what you are saying here. Assume the following:

CREATE TABLE PARENT
( a int not null primary key );

CREATE TABLE CHILD
( b int not null primary key
, a int not null 
,    constraint fk foreign key (a) 
         references PARENT (a) );

insert into PARENT (a) values (1),(2);

-- What should the default value of a be?
insert into CHILD (b) values (1); 


A foreign key is a rule that makes sure that you use a valid value for the column(s) involved. If you want a default value for a in CHILD you can add another constraint (I'm not sure why default values are considered to be constraints):

CREATE TABLE CHILD
( b int not null primary key
, a int DEFAULT 1 not null 
,    constraint fk foreign key (a) 
         references PARENT (a) );


Without that it is impossible for the DBMS to know what you mean when you don't provide a value for an attribute.

EDIT: Add info on how to retrieve last generated value

If you want to inspect what was generated in the PARENT table, and use that value for the CHILD table, you can use a function LAST_INSERT_ID():

CREATE TABLE PARENT
( a int not null AUTO_INCREMENT primary key
, c int not null );

CREATE TABLE CHILD
( b int not null primary key
, a int DEFAULT 1 not null 
,    constraint fk foreign key (a) 
         references PARENT (a) );

insert into PARENT (c) values (1);
insert into CHILD (b,a) select 1, LAST_INSERT_ID();


or

insert into CHILD (b,a) values (2, LAST_INSERT_ID());