Let's say a new instance of the latest (2.2.224) version of H2 is run via:
java -jar h2-2.2.224.jar
once the h2-console is reached and the following sample table is created:

create table some_table
(
    id int                not null primary key,
    a  int                not null,
    b  varchar(30),
    c  varchar(20),
    constraint some_table_constraint unique nulls not distinct (a, b)
);

the query:

select NULLS_DISTINCT 
from information_schema.indexes 
where table_name='SOME_TABLE' and index_name like 'SOME_TABLE_CONSTRAINT%';

returns NO (as expected).

However, once the following statement is executed
alter table some_table drop column c;
the previously mentioned select query
returns YES (surprisingly).

The NULLS_DISTINCT property value is somehow lost in the process and considering that the dropped column c was not a part of the constraint it is a bug - a rather hard-to-find and dangerous (if H2 was used on the prod environment) one.